improving ventricular late potentials detection ...

IMPROVING VENTRICULAR LATE POTENTIALS DETECTION EFFECTIVENESS by

Alberto Taboada Crispí B.Sc. (Electronic Engineer), Universidad Central de Las Villas (UCLV), Cuba, 1985 M.Sc. (Electronics), UCLV, Cuba, 1997 A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of

Doctor of Philosophy in the Department of Electrical and Computer Engineering

Supervisors:

Dennis F. Lovely, PhD, Electrical and Computer Engineering Juan V. Lorenzo Ginori, PhD, Univ. Central de Las Villas, Cuba

Examining Board:

Phillip A. Parker, PhD, Electrical and Computer Engineering Marilyn Hodgins, PhD, Nursing Ed Biden, PhD, Mechanical (Chairperson)

External Examiner:

Pierre Savard, PhD, Université de Montréal

Chair:

Gwendolyn Davies, PhD, Dean of Graduate Studies

This thesis is accepted.

________________________ Dean of Graduate Studies

THE UNIVERSITY OF NEW BRUNSWICK February 2002 © Alberto Taboada Crispí, 2002

Dedication

To my family and friends

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Abstract

Abstract Ventricular late potentials (VLPs) are low-amplitude, wideband-frequency waveforms that appear in the high-resolution electrocardiogram of patients with some cardiac diseases. VLP detection and analysis represents a prominent non-invasive marker for cardiac and cardiac related diseases. In a VLP diagnostic system, it is necessary to implement some noise-diminishing strategies to improve the SNR. Later, some methods to obtain relevant information on VLPs have to be applied. Time domain and frequency domain analyses have been the methods traditionally used. More recently, great interest has been focused on timefrequency analysis techniques. The global objective of this investigation was to improve VLP detection, while obtaining computationally affordable algorithms that could be implemented in computer-based HRECG (high-resolution electrocardiogram) analysers. This research proposes novel pre-processing and processing schemes to improve VLP detection in the noisy ECG environment. A HRECG database was created and rigorous simulations of the HRECG records, VLP waveforms, and noise and interference were incorporated to test every algorithm. A novel powerline interference canceller, based on an isoelectric interval detector, proved to diminish the interference better than traditional cancellers, without appreciable distortion of the ECG signal. A QRS detector, based on the double-level algorithm and cross-correlation adjustment, used a new composite channel to obtain better precision. To complete the pre-processing, an FIR high-pass filter combining an all-pass and a

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Abstract

binomial low-pass filter outperformed other previous FIR designs for VLP detection. The time-domain analysis improved robustness and repeatability by using a new modified signal-averaging (MSA) scheme, which is a combination of mean and median filtering.

A novel adaptive enhancer with MSA and maximum absolute value

“averaging” was designed to obtain certain beat-to-beat information and to emphasise the boundaries of the QRS complex. In addition, a novel 2-D VLP detection scheme was implemented, including stationary wavelet transform (SWT) denoising, Canny edge detection, and moment-based feature extraction. The number of heartbeats needed for the processing algorithms was reduced 5 times approximately. The new algorithms can handle certain non-stationary environments and provide beat-to-beat information. The results show improvement in the sensitivity and specificity.

All this will have, consequently, a direct impact on the lives of many

individuals.

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Acknowledgment

Acknowledgment The author would like to thank Dr. Juan V. Lorenzo-Ginori, co-director of the UNBUCLV Project, for giving him the opportunity of studying in Canada and for trusting him all the way through. He shows gratitude to Dr. Lorenzo-Ginori as well for being one of his supervisors and contributing to his work with encouraging comments. The author would also like to express thanks to his other supervisor, Dr. Dennis F. Lovely, for his valuable guidance and support. The author wants to emphasize that this project could have never been carried out without the understanding and patience of his beloved family. The education that his parents, Marta and Alberto, provided him was vital. They, his wife Nery, and the rest of his family deserve the greatest gratitude. The author wishes to express his sincere appreciation to the professors at the Electrical Engineering Faculty, UCLV, who replaced him in several activities during these long months. His professors there, and here at UNB, inspired him with their example. The author would also like to recognize the friendship and solidarity of the students and staff at the Institute of Biomedical Engineering/UNB and CEETI/UCLV. During the data collection, it was crucial the help from the Cardio Centre, the University Hospital, and the City Hospital of Santa Clara, Cuba. Many of their staff members joined their post-MI patients as subjects of this investigation. The author acknowledges the financial support from CIDA.

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Table of Contents

Table of Contents Abstract

............................................................................................................ iii

Acknowledgment .............................................................................................................. v Table of Contents ............................................................................................................. vi List of Tables

.............................................................................................................. x

List of Figures

............................................................................................................. xi

List of Symbols, Nomenclature and Abbreviations .................................................... xiv

Chapter 1 -

Introduction ........................................................................................ 1

1.1 Cardiovascular disease and sudden cardiac death ................................................. 1 1.1.1 SCD treatments........................................................................................... 3 1.1.2 Need of stratification techniques ................................................................ 4 1.2 Non-invasive versus invasive diagnostic techniques............................................. 6 1.2.1 Invasive technique: Electrophysiological Studies ...................................... 6 1.2.2 Non-invasive techniques............................................................................. 7 1.2.3 Indexes of effectiveness.............................................................................. 9 1.2.4 SCD model and combination of techniques ............................................. 12 1.3 Ventricular Late Potentials (VLPs) ..................................................................... 13 1.3.1 Origin of VLPs ......................................................................................... 13 1.3.2 VLPs and cardiac care .............................................................................. 17 1.3.3 Characteristics of VLPs. Why are they so difficult to detect?................. 20 1.4 Objectives ............................................................................................................ 25 1.5 Thesis outline....................................................................................................... 26 Chapter 2 -

Current clinical and research approaches ..................................... 28

2.1 Introduction ......................................................................................................... 28 2.2 Instrumentation requirements .............................................................................. 29 2.3 Signal enhancement techniques........................................................................... 37 2.3.1 Introduction .............................................................................................. 37 2.3.2 Coherent averaging................................................................................... 41 2.3.3 Optimal filtering and weighting averaging............................................... 44 2.3.4 Adaptive filtering...................................................................................... 46 2.3.5 High-Order Spectrum ............................................................................... 49 2.3.6 Denoising with Wavelets.......................................................................... 50 2.4 Detection/analysis................................................................................................ 50 2.4.1 Time domain............................................................................................. 51 2.4.2 Frequency domain .................................................................................... 54 2.5 Summary.............................................................................................................. 61

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Table of Contents

Chapter 3 -

Multi-dimensional representations in VLP studies....................... 63

3.1 First attempts ....................................................................................................... 63 3.2 Pre-processing for VLP time-frequency analysis................................................ 64 3.3 Desirable properties of the time-frequency representations ................................ 66 3.4 Classification of time-frequency analysis techniques ......................................... 70 3.4.1 Time-varying models................................................................................ 70 3.4.2 Linear time-frequency distributions ......................................................... 72 3.4.3 Bilinear time-frequency distributions....................................................... 74 3.4.4 Signal-dependent kernel TFDs ................................................................. 81 3.5 Information extraction from t-f images of the HRECG ...................................... 83 3.6 Wavelet transform as a special linear TFR.......................................................... 85 3.6.1 Orthogonal wavelets and multi-resolution scheme .................................. 87 3.6.2 Wavelet Packets as a generalization of the wavelet decomposition......... 91 3.6.3 Bi-dimensional WP analysis..................................................................... 92 3.6.4 Wavelet denoising .................................................................................... 93 3.6.5 Wavelet families ....................................................................................... 97 3.7 Summary............................................................................................................ 100 Chapter 4 -

HRECG database design ............................................................... 103

4.1 Introduction ....................................................................................................... 103 4.2 Front-end and acquisition process ..................................................................... 104 4.2.1 Front-end hardware................................................................................. 105 4.2.2 Front-end software.................................................................................. 107 4.2.3 Front-end settings ................................................................................... 108 4.2.4 HRECG data files ................................................................................... 109 4.3 General information of the DSP software ......................................................... 110 4.4 HRECG database............................................................................................... 112 4.4.1 Statistics.................................................................................................. 113 4.4.2 Noise characterisation............................................................................. 115 4.5 HRECG simulations .......................................................................................... 120 4.5.1 HRECG basic waveforms....................................................................... 121 4.5.2 VLP records............................................................................................ 122 4.5.3 Noisy records.......................................................................................... 124 4.5.4 Reproducibility assessment .................................................................... 125 4.5.5 Summary................................................................................................. 126 4.6 Summary........................................................................................................... .127 Chapter 5 -

ECG pre-processing algorithms.................................................... 129

5.1 Introduction ....................................................................................................... 129 5.2 Isoelectric interval detector ............................................................................... 130 5.3 Powerline interference cancellation................................................................... 132 5.3.1 Conventional and adaptive notch filters ................................................. 133 5.3.2 New powerline interference canceller .................................................... 137 5.3.3 Evaluation and discussion ...................................................................... 139

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Table of Contents

5.4 QRS detector...................................................................................................... 146 5.4.1 Enhanced double-level algorithm........................................................... 147 5.4.2 Cross-correlation fine adjustment........................................................... 151 5.4.3 Evaluation and discussion ...................................................................... 152 5.5 High-pass filter .................................................................................................. 160 5.5.1 Enhanced Simson approach.................................................................... 160 5.5.2 FIR filters................................................................................................ 162 5.5.3 High-pass filter implementation ............................................................. 163 5.5.4 Performance with test signals ................................................................. 168 5.6 Summary............................................................................................................ 170 Chapter 6 -

VLP processing techniques............................................................ 172

6.1 Introduction ....................................................................................................... 172 6.2 Enhanced time domain analysis ........................................................................ 173 6.2.1 Flexible analysis window ....................................................................... 174 6.2.2 Reduction of respiration effects by lead normalization.......................... 175 6.2.3 Modified Signal Averaging (MSA)........................................................ 178 6.2.4 High pass filtering options...................................................................... 192 6.2.5 Flexible analysis ..................................................................................... 192 6.2.6 Presentation of the results....................................................................... 193 6.2.7 Modified signal averaging versus coherent averaging ........................... 194 6.3 Adaptive enhancer plus MSA for beat-to-beat VLP detection.......................... 199 6.3.1 Initial ALE + MSA prototype................................................................. 199 6.3.2 Limitations of the initial ALE + MSA prototype ................................... 201 6.3.3 New adaptive enhancer with modified signal averaging........................ 201 6.3.4 Adaptive enhancer evaluation ................................................................ 205 6.4 2-D VLP detection scheme................................................................................ 210 6.4.1 Noise removal from the 2-D HRECG signal.......................................... 210 6.4.2 Detection of onset and offset from the 2-D HRECG signal ................... 214 6.4.3 Feature extraction from the 2-D HRECG signal .................................... 215 6.4.4 Detection/classification .......................................................................... 217 6.4.5 2-D analysis evaluation .......................................................................... 218 6.5 Conclusions ....................................................................................................... 225 Chapter 7 7.1 7.2 7.3

Conclusions ..................................................................................... 228

Summary............................................................................................................ 228 Original Contributions....................................................................................... 236 Limitations of this work and directions of future research................................ 238

References

.......................................................................................................... 241

Appendix A: Consent form .......................................................................................... 254 Appendix B: Patients .................................................................................................... 256

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Table of Contents

Appendix C: Healthy Volunteers ................................................................................ 260 Appendix D: Noise characterisation of raw data ....................................................... 262 Appendix E: Noise characterisation of filtered data ................................................. 282 Appendix F: Interference cancellation evaluation .................................................... 297 Appendix G: QRS detection evaluation. Influence of noise and interference........ 303 Appendix H: QRS detection evaluation. Enhanced double-level algorithm .......... 305 Appendix I: QRS detection evaluation. Cross-correlation adjustment .................. 309 Appendix J: 2-D VLP detection................................................................................... 313 Vita

.......................................................................................................... 330

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List of Tables

List of Tables Table 3.1- Characteristics of the most popular wavelet families........................................98 Table 5.1- Correlation coefficients (and p-values) between the features from the clean signal (s) and the noisy (sn) and estimated signals (se1~4)........................................145 Table 6.1- Input signals and matrices used by the MSA, as well as the output signals of the MSA (y[j]), coherent averaging (xave[j]), and this with 2-sample MA (xMA[j]). .183 Table 6.2- Linear regression analysis results....................................................................224

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List of Figures

List of Figures Figure 1.1- Incidence of SCD in a global population and in a group at higher risk. .......... 5 Figure 1.2- Typical results of SAECG studies for risk stratification of SCD after MI. ... 11 Figure 1.3- ECG signal (one beat or complex P-QRS-T, v20, Y-lead). ........................... 14 Figure 1.4- Conductive system of the heart. ..................................................................... 14 Figure 1.5- Re-entrant phenomenon in damaged section of myocardium........................ 16 Figure 1.6- Noise and interference corrupting the ECG. .................................................. 22 Figure 1.7- Power spectral density of the ECG, QRS complex and P and T waves......... 24 Figure 2.1- System for detection and analysis of VLPs.................................................... 28 Figure 2.2- 12-lead system commonly used in clinical ECG. .......................................... 30 Figure 2.3- XYZ orthogonal lead system recommended for VLP studies. ...................... 31 Figure 2.4- Instrumentation requirements for VLP acquisition (one channel)................. 37 Figure 2.5- Signal-to-noise ratio enhancement................................................................. 38 Figure 2.6- Isolation of segments of interest from the ECG sequence. ............................ 39 Figure 2.7- Coherent averaging for VLP enhancement showing the trigger jitter effect. 42 Figure 2.8- Cutoff frequency of the trigger jitter equivalent filter. .................................. 43 Figure 2.9- Adaptive filter enhancing set-up. ................................................................... 47 Figure 2.10- Performance of conventional and bidireccional high-pass filtering [182]... 52 Figure 2.11- Features in VLP time-domain analysis (p38)............................................... 53 Figure 2.12- PSD estimation methods described in the literature. ................................... 57 Figure 2.13- Implicit rectangular window and Blackman-Harris window (fs=1kHz). ..... 59 Figure 2.14- Typical VLP frequency domain analysis (X-lead, p18)............................... 60 Figure 3.1- STM of the X-lead (fv03) by following the procedure described in [91]...... 64 Figure 3.2a- Time domain analysis of the SAECG (X-lead, p15b).................................. 79 Figure 3.2b- Analysis of a high-pass filtered SAECG (X-lead, p15b) by different TFDs. .................................................................................................................................... 80 Figure 3.3- Analysis of a SAECG (X-lead, p15b) by the adaptive optimal-kernel TFR.. 82 Figure 3.4- Multiple level decomposition (analysis) by the pyramid algorithm. ............. 88 Figure 3.5- Six-level decomposition of the SAECG (Y-lead, fp26) showing the original signal (s), approximations (a), details (d) and coefficients (cfs)................................ 89 Figure 3.6- Reconstruction algorithm (synthesis)............................................................. 90 Figure 3.7- Three-level WP decomposition tree............................................................... 91 Figure 3.8- Bi-dimensional WP decomposition (2 levels)................................................ 93 Figure 3.9- Wavelet denoising scheme............................................................................. 94 Figure 3.10- Analysis of SAECG with the Morlet wavelet (Y-lead, fp26). ................... 100 Figure 4.1- Analog front-end. ......................................................................................... 105 Figure 4.2- Data conversion and storing......................................................................... 105 Figure 4.3- Main window of DaqView 7.0..................................................................... 106 Figure 4.4- Window of Daq_216A software. ................................................................. 107 Figure 4.5- Example of descriptor file (.IO$). ................................................................ 109 Figure 4.6- Risk stratification software main window.................................................... 111

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List of Figures

Figure 4.7- HRECG embedded noise in the time domain (p50, X-lead)........................ 116 Figure 4.8- Estimated Power Spectral Density of the noise (p50, X-lead)..................... 117 Figure 4.9- Synthesised VLP for the XYZ leads in the time and frequency domains.... 123 Figure 5.1- Isoelectric intervals detected automatically (p50, X-lead, 1.2-3.6sec). ....... 131 Figure 5.2- Characteristics of a digital notch filter with fl=60Hz and r=0.98. ............... 134 Figure 5.3- New adaptive powerline canceller. .............................................................. 137 Figure 5.4- Estimated PSD of the noise (p50, X-lead) after filtering. ............................ 139 Figure 5.5- Evaluation of interference canceller procedures (X-lead, fv11, n2)............. 143 Figure 5.6- Evaluation of powerline cancellation algorithms (review of Appendix F).. 144 Figure 5.7- Enhanced double-level algorithm (EDL). .................................................... 148 Figure 5.8- Determining the fiducial marks, with a double-level algorithm (v03, Y-lead). .................................................................................................................................. 149 Figure 5.9- Cross-correlation adjustment and PVC and grossly noisy heartbeats rejection. .................................................................................................................................. 150 Figure 5.10- Selection of the initial template in the PC-based system (v03, Y-lead)..... 151 Figure 5.11- Performance of the algorithms at different SNRs. ..................................... 155 Figure 5.12- Signal-to-noise ratio of the signals included in the study. ......................... 158 Figure 5.13- Performance of the algorithms with different reference channels. ............ 159 Figure 5.14- Magnitude response, group delay and impulse response of the 4-order Butterworth high-pass filter with cutoff frequency of 40Hz.................................... 162 Figure 5.15- Changes of the cutoff frequency with the order M. ................................... 164 Figure 5.16- Noise attenuation as a function of the order M. ......................................... 165 Figure 5.17- Widening effect as a function of the order M. ........................................... 166 Figure 5.18- Variance and bias of the frequency response as a function of M............... 167 Figure 5.19- Characteristics of the new filter with order M=80. .................................... 168 Figure 5.20- Assessment of filters with different input test signals. .............................. 169 Figure 6.1- Enhanced time domain analysis. .................................................................. 174 Figure 6.2- Typical distribution of heartbeat windows within a respiration period. ...... 176 Figure 6.3- Respiration effects before and after applying lead normalization. .............. 177 Figure 6.4- Frequency response for 3-sample and 2-sample MA systems (fs=1kHz). ... 179 Figure 6.5- Input and output signals from the averaging methods. ................................ 184 Figure 6.6- Normalised cross-correlations of the noise in the isoelectric segments....... 187 Figure 6.7- Values of σo versus values of d.................................................................... 188 Figure 6.8- Values of k versus values of d...................................................................... 189 Figure 6.9- Values of variance σo2 versus number of heartbeats N. ............................... 191 Figure 6.10- Analysis window of the PC-based system (fp16, V). ................................ 193 Figure 6.11- MSA versus signal averaging (each combined with FIR filtering, M = 80) for N=60. .................................................................................................................. 196 Figure 6.12- MSA versus signal averaging (each combined with FIR filtering, M = 80) for SNR=0dB in the VLP region.............................................................................. 198 Figure 6.13- Adaptive line enhancing plus modified signal averaging [202]................. 200 Figure 6.14- New adaptive enhancer with modified signal averaging. .......................... 203 Figure 6.15- Example of the performance of the adaptive enhancer + MSA with a noisy variable-VLP record (Z-lead of nVLPj1).................................................................. 206

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List of Figures

Figure 6.16- Example of the performance of the adaptive enhancer + MSA with a noisy non-VLP record (Z-lead of n1). ................................................................................ 207 Figure 6.17- Absolute value of the “averaged” signals compared to one ideally clean beat. .................................................................................................................................. 209 Figure 6.18- 2-D VLP detection scheme. ....................................................................... 211 Figure 6.19- Decomposition of the original ideally clean image (Z-lead of cVLPj1)..... 218 Figure 6.20- Decomposition of the original noisy image (Z-lead of nVLPj1). ............... 219 Figure 6.21- Decomposition of the denoised noisy image (Z-lead of nVLPj1). ............. 220 Figure 6.22- HRECG images before and after denoising (cVLPj1 top and nVLPj1 bottom). .................................................................................................................................. 221 Figure 6.23- Masks for feature extraction obtained by edge detection based algorithm from a clean and a denoised noisy image (cVLPj1 top and denoised nVLPj1 bottom). .................................................................................................................................. 222

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List of Symbols, Nomenclature and Abbreviations

List of Symbols, Nomenclature and Abbreviations φ

scale function (WT)

φxx

autocorrelation function of x

φxy

cross-correlation function of x and y

Φxx

PSD of x

Φxy

cross PSD of x and y

Φa

kernel for the Affine class TFDs

Φc

frequency-Doppler dependent kernel for the Cohen class TFDs

ϕ

phase difference between interference in main input and reference input

ϕa


ϕc

time-lag dependent kernel for the Cohen class TFDs

ψ

mother or basic wavelet (WT)

ψa


ψc

t-f dependent kernel for the Cohen class TFDs

Ψa


Ψc

lag-Doppler dependent kernel for the Cohen class TFDs

λ

forgetting factor

µ

step-size parameter

εk

error at sample k

ν

Doppler in TFDs

τ

lag in TFDs

τ

misalignment

τ

translation parameter in WT

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τx(f)

group delay of the signal x

∞

infinite

ρ

optimal one-weight filter (between 0 and 1)

θ

remaining noise after signal enhancing

α

standard deviation of a Gaussian process

αc

parameter to control the kernel concentration around the origin

γ

the largest eigenvalue of the autocorrelation matrix (adaptive filtering)

γ

threshold level in the wavelet denoising scheme

γd

threshold level in the wavelet denoising scheme for diagonal details

γh

threshold level in the wavelet denoising scheme for horizontal details

γv

threshold level in the wavelet denoising scheme for vertical details

∆f

frequency resolution

σiso

standard deviation of noise (isoelectric segment)

σo

standard deviation of output noise (after processing)

σn

standard deviation of n

σn 2

variance of n

σX

standard deviation of misalignment using X-lead reference channel

σXY

standard deviation of relative misalignment using X-lead and Y-lead reference channels

µV

micro Volt(s)

Γ{⋅}

rounds ⋅ the nearest integer towards zero

|⋅|

absolute value of ⋅

1-D

mono-dimensional

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2-D

bi-dimensional

3-D

three-dimensional

A

amplitude of the modulation due to respiration

a

dilation/contraction parameter (WT)

a

output of the ALE in the ALE+MSA prototype

A/D

analog-to-digital

A1

area between |H(f)| and all-pass filter

A2

area below |H(f)|

Ad

differential gain

AF

ambiguity function

Ag/AgCl

silver/silver chloride

Ai

gain of the i-th stage

ALE

adaptive line enhancing

Amp.

amplifier

ANN

artificial neural networks

APWF

A Posteriori Wiener Filter

AR

auto-regressive

arctan

arc tangent

ARMA

auto-regressive moving-average

att

attenuation of the noise

AV

atrio-ventricular

aVF

unipolar augmented lead

AVID

the Amiodarone Versus Implantable Defibrillator trial

aVL


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aVR


b

number of bits (of the A/D converter)

bθ

bias of remaining noise

BBB

bundle branch block

Bw

bandwidth (Bw = fh – fl)

C

amplitude of the reference sinusoid (in powerline cancellation)

C

coefficients of the WT

C

composite channel used as reference by the EDL algorithm

c

shrunk coefficients (wavelet-based denoising)

c1~34

clean non-VLP 5min test records

CC

correct classification

CCA

cross-correlation adjustment

ch

shrunk coefficients after hard thresolding

CMRR

common-mode rejection ratio

Cov

covariance

cs

shrunk coefficients after soft thresholding

CSA

Canadian Standards Association

css

shrunk coefficients after semi-soft thresholding

CVD

cardiovascular disease

cVLP1~34

clean fixed-VLP 5min test records

cVLPj1~34

clean variable-VLP 5min test records

CWT

continuous wavelet transform

Cxh

cross-correlation coefficients of the signals x and h

D

DC level representing the baseline wandering

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d

number of displaced samples to take into account for MSA computation

D1~3

basic bipolar leads

dB

decibel(s)

DC

direct current

DFT

discrete Fourier transform

DSP

digital signal processing

DWT

discrete wavelet transform

E[⋅]

expected value of ⋅

ECG

electrocardiograph, electrocardiographic, electrocardiogram

EDL

enhanced double-level algorithm

EMG

electromyography, electromyographic

EPS

electrophysiologic study

ESB

equivalent statistical bandwidth

sˆ

estimated signal

exp

exponential

f

frequency

F

left foot (in lead systems)

F{⋅}

Fourier transform of ⋅

F-1{⋅}

inverse Fourier transform of ⋅

fc

cutoff frequency

FET

field effect transistor

FFT

fast Fourier transform

fh

cutoff (upper) frequency

FIR

finite impulse response

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fixed-VLP

HRECG record including VLPs that do not change from beat to beat

fl

cutoff (lower) frequency

fl

powerline frequency

FN

false negative

FP

false positive

fs

sampling frequency

FT

Fourier transform

fx(t)

instantaneous frequency of the signal x

GUI

graphical user interface

H(f)

frequency response

h[k]

impulse response

Hhp

HPF magnitude response

hlp

LPF impulse response

Hlp

LPF magnitude response

Hopt(f)

optimal filter frequency response

HPF

high-pass filter(ing)

HPFd

high -pass filter(ing) for decomposition

HPFr

high -pass filter(ing) for reconstruction

HRECG

high resolution ECG

HRV

heart rate variability

HT

Hilbert transform

Htj(f)

equivalent trigger jitter frequency response

Hz

Hertz

ICD

implantable cardioverter-defibrillator

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ICU

intensive care unit

IDFT

inverse discrete Fourier transform

IHD

ischemic heart disease

IIR

infinite impulse response

ISO

isoelectric segment

Iso.

Isolation

iso0

output of the isoelectric interval detector

k

security factor, between zero and one, for d (or N) estimation in MSA

kHz

kilo Hertz

L

left hand (in lead systems)

L

levels of decomposition in the WT (or WP)

LASd

low-amplitude signal duration

LMS

least mean squares

LMU

Ludwig Maximilians University

ln

natural logarithm

log10

decimal logarithm

LPF

low-pass filter(ing)

LPFd

low-pass filter(ing) for decomposition

LPFr

low-pass filter(ing) for reconstruction

lsa

samples taken from the left of fiducial marks to segment the HRECG

LSB

low significant bit

LVEF

left ventricular ejection fraction

M

filter order

m

matrix for the MSA computation

xx


M

number of samples

m2v

matrix-to-vector conversion

MA

moving-average

MADITT

the Multi-centre Automatic Defibrillator Implantation Trial

max

maximum

med(⋅)

median of ⋅

MI

myocardial infarction

min

minimum

min

minute(s)

MIT

Massachusetts Institute of Technology

MIT-BIH

MIT-Beth Israel Hospital (ECG database)

ML

maximum likelihood

ms

millisecond(s)

MSA

modified signal averaging

MSE

mean square error

MUSIC

multiple signal classification

MUSTT

the Multi-centre UnSustained Tachycardia Trial

mV

milli Volt(s)

n

noise

N

number of heartbeats

n1~34

noisy non-VLP 5min test records

NF

normality factor

Ni

noise of the i-th stage

NMSA

number of samples involved in the arithmetic mean of the MSA

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non-VLP

HRECG record without including VLPs

NP

negative predictability

nsVT

non-sustained ventricular tachycardia

nV

nano Volt(s)

nVLP1~34

noisy fixed-VLP 5min test records

nVLPj1~34

noisy variable-VLP 5min test records

O

order of the basic wavelet

o1

vector output of the adaptive enhancer

o2

matrix output of the adaptive enhancer

o3

vector output of the adaptive enhancer + MAV

pA

pico Ampere(s)

PC

personal computer

Pn

power of noise

PP

positive predictability

PQ

segment on the ECG

P-QRS-T

waves on the ECG

PSD

power spectral density

PTCA

percutaneous transluminal coronary angioplasty

PVC

premature ventricular contraction (or complex)

PWD

pseudo Wigner distribution

Q

quality factor

q

trimming parameter used in the MSA computation

QMF

conjugate quadrature filters or quadrature mirror filters

QRS

complex on the ECG

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QRSd

duration of the filtered QRS

r

radius of poles in notch filtering design

r

reference signal

R

right hand (in lead systems)

RLS

recursive least squares

rms

root-mean-square

RMS40

Root mean square voltage of the last 40ms of the filtered QRS

RR

distance (interval) between two consecutive QRS complexes

rsa

samples taken from the right of fiducial marks to segment the HRECG

s

clean signal

S/H

sample and hold

SA

sino-atrial

SAECG

signal-averaged ECG

SCD

sudden cardiac death

SCD-HeFT

the Sudden Cardiac Death Heart Failure Trial

SE

sensitivity

sec

second(s)

sgn(⋅)

sign of ⋅

SNR

signal-to-noise ratio

SP

specificity

ST

segment on the ECG

std

standard deviation

Std

time-domain analysis standard method (Simson)

STFT

short-time Fourier transform

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STM

spectro-temporal mapping

sVT

sustained ventricular tachycardia

SW

switch

SWD

smoothed Wigner distribution

SWT

stationary WT

symlet O

quasi-symmetric wavelet of order O

t

time

ta

fiducial marks

ta’

corrected fiducial marks

tC

fiducial marks using composite reference channel

tf

“final” fiducial marks (obtained from noisy records)

t-f

time-frequency

TFD

time-frequency distribution

TFR

time-frequency representation

ti

“initial” fiducial marks (obtained from clean records)

TN

true negative

TP

true positive

TSAF

time-sequenced adaptive filtering

tX

fiducial marks using X-lead reference channel

Tx(t,f)

TFR of the signal x

tY

fiducial marks using Y-lead reference channel

tZ

fiducial marks using Z-lead reference channel

V

cardiac vector magnitude

V1~6

pre-cordials or chest leads

xxiv


v2m

vector-to-matrix conversion

variable-VLP HRECG record including VLPs that change position from beat to beat Vcm

common mode signal (used as a reference for adaptive cancellation)

VF

ventricular fibrillation

VLP-

not exhibiting VLPs

VLP

ventricular late potential

VLP+

exhibiting VLPs

VLP-ISO

difference between the variances in the “VLP” and the isoelectric regions

Vlsb

quantisation level (low significant bit value)

Vmax

maximum analog input

Vp

peak voltage

VT

ventricular tachycardia

W

filter weights

w

weighting matrix for MSA computation

WC

whitening coefficient

WD

Wigner distribution

wos

displacement or offset of the analysis window to correct the fiducial marks

WP

wavelet packets

WT

wavelet transform

WVD

Wigner-Ville distribution

x

acquired signal (signal plus noise), input signal

X

individual orthogonal lead

X(f)

signal in the frequency domain (Fourier transform)

x(t)

continuous signal in the time domain

xxv


x[k]

discrete (sampled) signal in the time domain

Xa

analytic signal (frequency domain)

xa

analytic signal (time domain)

xave

coherent averaging output

xi,j

the j-th sample of the i-th isolated segment (heartbeat)

xMA

coherent averaging plus 2-sample MA output

XYZ

orthogonal bipolar system

Y


y

output signal

Z


xxvi

Chapter 1- Introduction

Chapter 1 - Introduction Cardiovascular disease (CVD) is the leading cause of death worldwide and sudden cardiac death (SCD) is responsible for 50%. Patients at risk for SCD have several treatments available to them. However, an accurate and non-invasive method to identify those at risk has been missing. Ventricular late potentials (VLPs) appear associated with ventricular tachycardia (VT) preceding most instances of SCD. Detection of VLPs has proved to have potential as a VT predictor, as well as a diagnostic marker for several cardiac abnormalities [33] [26] [47]. Current VLP detection techniques, however, present numerous limitations. Therefore, to be successfully used in a clinical environment, substantial improvement is required. This is the primary objective of this thesis. This introductory chapter includes the fundamentals needed to understand the motivations for this work, and briefly describes the organisation of the thesis.

1.1 Cardiovascular disease and sudden cardiac death CVD is a major cause of death all over the world. The incidence rates are sex- and agedependent and can change from one country to another, but they are always impressive. To mention some examples published in [95], around 1995, mortality rates for CVD in men was 232.7 deaths per 100 000 population in Japan, the lowest reported, and as high as 1 051.7 per 100 000 in the Russian Federation. In Canada, 36% of all deaths are due to CVD. Of these, nearly 56% are from ischemic heart disease (IHD). More specifically,

1


of the deaths due to IHD, 50% can be attributed to myocardial infarction (MI) [95]. Major risk factors for CVD are well known, but no significant improvements have been reached to keep them under control. The epidemic of CVD will continue in the years to come, due to the high prevalence of smoking, physical inactivity, high blood pressure, dyslipidemias, obesity and diabetes all around the world. To make things worse, the number of persons suffering from CVD is expected to grow because of the increasing numbers of the elderly population, which is the most likely to develop cardiovascular problems. SCD is the term given to natural death from cardiac causes, with an abrupt loss of consciousness preceding the acute symptoms, in a person with or without diagnosed cardiopathy [105]. Most SCDs are thought to be initiated by VT and/or ventricular fibrillation (VF), two of the most serious types of cardiac arrhythmia [155]. These lethal arrhythmias affect the main pumping chambers of the heart, the ventricles. In VT, the ventricles beat too fast, compromising their ability to pump blood. VTs consist of 3 or more consecutive ventricular depolarisations at rates of 100 beats per minute or higher; they can be classified as non-sustained ventricular tachycardias (nsVT), when they disappear spontaneously in less than 30 seconds, or sustained ventricular tachycardias (sVT), when last longer. In VF, the ventricles contract in a disorganised fashion that results in total loss of their blood-pumping action. VF, unless interrupted by an electrical shock (defibrillation), is fatal and is the immediate cause of SCD in the majority of cases. It is important to note that VT may progress into VF.

2


Half of the deaths due to CVD can be classified as SCD, that is, around 10% to 15% of all natural deaths. In the United States alone, SCD affects around 500 000 people each year, almost 2 cases per 1 000 inhabitants and claims the lives of about 70% of them [105] [17].

These figures, although generated from calculations and likely to be

inaccurate, have gone unchanged for 20 years. 1.1.1 SCD treatments Most people who suffer SCD can be saved if they are resuscitated promptly. Different treatments have been used to handle VT and SCD, among them, antiarrhythmic drug therapy to prevent and control arrhythmias, surgical procedures (catheter ablation) to destroy arrhythmic substrate [96] and implantation of antitachycardiac devices like the implantable cardioverter-defibrillator (ICD). The latter is a device that detects when the heart goes into VT or VF and ends the arrhythmia by applying electrical shocks to the heart [172]. In recent years, treatments have been improved and many studies have tried to find the best choice [105] [172] [74] [156]. Until now, there has been controversy as to whether pharmacotherapy can work as well as the ICD [172] [156]. In 1997, a large clinical study, the Amiodarone versus Implantable Defibrillator trial (AVID) [15], had to be stopped prematurely because it showed that patients who received ICD devices had a much lower mortality than those treated with amiodarone or sotalol (another antiarrhythmic drug).

For those patients who cannot receive an ICD,

amiodarone is an excellent treatment option; however, based on available data, AVID and some other extensive trials like the Multi-centre Automatic Defibrillator Implantation Trial (MADIT) and the Multicentre UnSustained Tachycardia Trial (MUSTT ) [154] [108] agree that the ICD device is the most effective treatment. At present, some more

3


detailed trials are progressing toward completion [154]. One of which, the Sudden Cardiac Death Heart Failure Trial (SCD-HeFT), is due to report in 2003 [108]. ICD therapy is expensive.

Therapies in medicine are generally considered “cost-

effective” if they cost less than $50 000 per year life saved [136] [48]. The preliminary figures for ICD plus doctor and hospital fees associated with the implantation and subsequent monitoring of the device can be in the range of $60 000 to $70 000 [17] and around $34 000 for drug therapy. On the other hand, antiarrhythmic drug therapy can have some unexpected side effects, like congestive heart failure and an increased risk of SCD, so it should be used with caution. Hence, identification of those patients at higher risk is imperative. From a clinical point of view, the challenge is to find who is really at risk of SCD and needs a particular kind of therapy from a general population with some lower risk factor [85]. 1.1.2 Need of stratification techniques SCD can occur in young people who have no history of heart disease until their death, but most often it occurs in people who have underlying heart disease. For instance, MIs, caused by diseased blood vessels in the heart, may leave patients much more prone to SCD. Survivors of cardiac arrest have a 35% chance of dying from SCD within a period of 2 years following the event [105]. Figure 1.1 compares the incidence of SCD in a global population and in a group at higher risk on a 3-year period after a serious cardiovascular episode, that is, survivors of cardiac arrest [105]. For the general population, the slope of survivors is constant with a value around -0.2% per year. However, looking at the higher risk group, the absolute value of

4


the slope significantly increases, mainly during the first year following the event. For this group, the risk of SCD is not linear over time, for example, about 50% of deaths within a period of 2 years after a MI happen during the first 6 months [105]. The slope of survivors, in the group at higher risk, reduces with time, tending to be closer to the one of groups at smaller risk. The use of the time as dimension to measure the risk allows a more efficient screening by reducing the population to the one at the highest risk.

105 100

Survivors (%)

95 90

General population Group at higher risk

85 80 75 70 65 60

0

0.5 1 1.5 Follow-up period (years)

2

2.5

3

Figure 1.1 Incidence of SCD in a global population and in a group at higher risk.

Even the group of patients recovering from a MI, which is at risk for SCD, is too numerous for ICD implantation, or antiarrhythmic drug therapy, in a 100% of the cases. Only around 4 to 6% of patients have an augmented risk for VT, VF, or SCD within 2 years following MI [17]. Some risk stratification techniques have to be applied to reduce the number of candidates for treatment to a reasonable value [85].

5


1.2 Non-invasive versus invasive diagnostic techniques 1.2.1 Invasive technique: Electrophysiological Studies Invasive electrophysiological studies (EPSs) have been the primary method used for investigating and treating VT for more than 20 years [220]. These studies can be used to determine the inducibility of VT and to estimate the efficacy of different antiarrhythmic drugs. Besides, EPSs can be used to guide radiofrequency ablation to destroy arrhythmic substrate, when it is present [197]. The EPS laboratory also has been used for the implantation of ICDs in recent years, even when these devices allow limited studies to be done non-invasively after being implanted. The incentive to perform an EPS previous to ICD implantation would be: •

to identify VT mechanisms such as bundle branch re-entry VT,

•

to predict future events, after estimating how inducible the VT is and

•

to optimise the ICD antitachycardia pacing parameters, after characterising the VT.

To perform an EPS [220], one to three multielectrode catheters are introduced into the right ventricle and, optionally, into the right atrium near to the bundle of His. The placing of these catheters, via the femoral veins, is guided by imaging techniques such as X-rays, magnetic resonance imaging, or spiral computed tomography.

Programmed

electrical stimulation, with a systemic variation in the pacing modes, stimulus-to-stimulus intervals and number of extra-stimulation pulses, is used in an attempt to induce a VT episode [156]. Sometimes during an EPS, electrograms are recorded directly from the heart chambers. 6


These electrograms have a signal magnitude in the order of 100 mV and they are not affected by external interference, providing a very high signal-to-noise ratio (SNR) record. EPSs require highly trained personnel [197], who have to operate several costly instruments [133] in an aseptic operating room. The surgical incision needed for the internal endocardial catheterisation carries associated dangers and it implies certain discomfort to the patient. In addition, this test is very expensive; the cost of a single case is approximately $1 700 [17]. 1.2.2 Non-invasive techniques Non-invasive methods to determine high-risk susceptibility for SCD include ambulatory electrocardiographic monitoring (ECG Holter) to analyse ventricular ectopy [26] [85] [17] [213] and heart rate variability (HRV) [85] [17].

Some other techniques are

baroreflex sensitivity testing, left ventricular ejection fraction (LVEF) measured in the echocardiogram, T-wave alternans and ventricular late potentials (VLPs) from the highresolution ECG (HRECG). All these tests are less expensive (around $300 [17]) and are less risky procedures than the EPSs, so many more patients could benefit from them. It has been suggested that around 88% of post-MI cases could be stratified with noninvasive procedures and only the remaining 12% would require EPSs [17]. Ventricular ectopy Ventricular ectopy is related to heartbeats resulting from an abnormal electrical focus in the ventricles, rather than from the natural pacemaker, the sino-atrial (SA) node. These particular beats are also called premature ventricular contractions (PVCs) and can be

7


easily distinguished from the normal beats, originating from the SA node, due to its broad QRS complex. The ambulatory ECG (Holter) allows the recording of a long segment of ECG activity, normally extending to 24 hours or longer. When performed during a lethal VT, it reveals a high density of VT episodes, often nsVT exceeding 10 beats, preceding the terminal one. PVCs can be detected in a Holter recording and are prognostic indicators of SCD. The number of PVCs higher than 10 per hour should be taken into account in the assessment [85]. PVCs and nsVT are considered trigger mechanisms initiating sVT, which evolves into VF and ends in SCD. Heart Rate Variability It has been suggested that both, the arrhythmic substrate and the trigger mechanism, can be modulated by the autonomic nervous system. The HRV (RR-interval variability) and the baroreflex sensitivity are non-invasive indexes of the autonomic nervous regulation [105]. It has been found that the HRV decreases (even to less than 20 ms) after a MI in patients prone to a SCD episode [85] [186] [153] [22]. Left Ventricular Ejection Fraction The left ventricular ejection fraction (LVEF) is the proportion of blood ejected from the left ventricle, the main pumping chamber of the heart, each time it beats. A normal healthy left ventricle ejects 55 to 70% of its contents during every heartbeat. Any condition that damages or kills heart muscle cells, such as a MI, can lower the LVEF. A way to measure the left ventricular dysfunction is to use the echocardiogram. If the LVEF calculated after a MI is less than 35%, then the chances are much higher for the

8


occurrence of SCD [85]. T-wave alternans Much more recently, the T-wave alternans test was introduced [99]. This diagnostic tool detects very small amplitude changes (~ 1 µV), on a beat-by-beat basis within the Twave. The ECG is recorded during biking or treadmill exercising, by using special electrodes. When electrical activity in the heart fluctuates between beats, this can cause electrical wavefronts to break up and recirculate, causing VT and VF. Patients with these tiny beat-to-beat fluctuations, that is, with the T-wave alternans, are at much higher risk of sVT and SCD than those without it. Ventricular Late Potentials Ventricular Late Potentials (VLPs), as well as the T-wave alternans, are associated with the arrhythmogenic substrate. VLPs are small signals that appear in the high-resolution ECG (HRECG) at the end of the QRS complex. A patient exhibiting VLPs is more prone to suffer from sVT and SCD than a healthy individual. The standard procedure to detect VLPs [26] uses the signal-averaged ECG (SAECG) to enhance the poor SNR of the segment of interest. This is the risk stratification technique that will be assessed and improved upon in this thesis. 1.2.3 Indexes of effectiveness In preventive medicine, as in the case of risk stratification for SCD in post-MI patients, several indexes are used to measure the effectiveness of a particular test. Sensitivity (SE) is a measure of the reliability of a screening test based on the proportion of patients with a specific disease − in this particular case, the patients suffering from sVT/VF and SCD −

9


who react positively (true positives, TPs) to the test. Higher SE implies fewer false negatives, FNs. SE contrasts with specificity (SP), which is the proportion of normals that react negatively (true negatives, TNs) to the test. Higher SP means fewer false positives, FPs. Some other useful parameters to evaluate a diagnostic test are the positive and the negative predictability (PP and NP, respectively), which are related to the group exhibiting and the group not exhibiting VLPs, respectively. To illustrate the previous parameters with numbers from actual cases, a compilation of 6 SAECG studies detailed in [85] will be used. Although not explicit in the paper, some figures and formulas can be easily deduced from the available data and they are included in Figure 1.2. The 6 studies grouped 1 068 post-MI patients, 342 of them with VLPs (VLP+) and 726 without (VLP-). After a follow-up period (around 1 year), 67 patients from the VLP+ group (TP = 67) and 20 from the VLP- group (FN = 20) developed sVT, VF, or died suddenly. In this global example, the SE, which is the percentage of VLP+ patients from the SCD population, is 77% (67/87). The SP, which is the percentage of VLP- patients from the non-SCD population, is 72% (706/981). The PP, which is the percentage of patients who developed life-threatening episodes from the VLP+ group, is 20% (67/342) and the NP, that is the percentage of non-SCD patients from the VLP- group, is 97% (706/726). The classifications were correct (CC) in 72% (773/1068) of the cases.

10


In a newer review of 13 SAECG analysis gathering almost 7 000 patients [17], the SE reported was 62%, SP = 78%, PP = 13% and NP = 98%.

TN

FN

TP

FP 706

275 67

20

VLP+ = TP+FP VLP- = TN+FN SCD = FN+TP nonSCD = TN+FP Total = TP+FP+TN+FN SE = TP/SCD = 1- FN/SCD SP = TN/nonSCD = 1- FP/nonSCD PP = TP/VLP+ = 1- FP/VLP+ NP = TN/VLP- = 1- FN/VLPCC = (TP+TN)/Total = 1- (FP+FN)/Total

Figure 1.2 Typical results of SAECG studies for risk stratification of SCD after MI.

The results of an individual study can change due to differences in the composition of the group (age, multiple infarctions or some other complications, LVEF, PVCs, etc.), instrumentation, criteria defining VLPs and the follow-up period [141]. SE is obviously wanted to be maximised in any preventive screening test such as VLP detection. If patients detected as VLP+ are going to be considered as at the highest risk for SCD and antiarrhythmic therapy will be implemented (implantation of an expensive ICD, or a drug therapy with possible side effects), then a very high SP must equally be achieved. A review of published reports from 1986 to 1998 [17] reveals that all non-invasive

11


stratification modalities, as well as the EPSs yield a low PP; none has proven useful enough by itself to predict occurrence of sVT or VF. To identify higher risk patients from the initial group under consideration, usually discrete thresholds are fixed for various parameters, for instance, QRSd > 110 ms on SAECG (see Section 2.4.1.). The PP can be increased by using tighter thresholds (e.g. QRSd > 120 ms rather than QRSd > 110 ms), but that could imply a lower SE due to increased FNs. Another solution is to repeat the test at different times during the day, based on the circadian variations of heart conditions [109]. 1.2.4 SCD model and combination of techniques An accepted model of SCD in coronary heart disease [105] includes a substrate for reentry (provided by a small LVEF and some other factors) [152], which is not selfsufficient to start and propagate a VT, and a trigger mechanism (as PVCs and nsVT) responsible for the initiation of VT. If the substrate exists, a VT can start in the presence of a trigger and, once started, it is self-sustaining. Both the substrate and the triggers are modulated by the autonomic nervous system [186]. Based on this model, a good risk stratification strategy should integrate an assessment of the substrate, the presence of triggers and the function of the autonomic nervous system. At present, EPSs, and/or the presence of VLPs, and T-wave alternans can identify the substrate (although these tests could be independent markers). The triggers are found and quantified by ambulatory ECG monitoring. HRV and baroreflex sensitivity testing can assess the state of the autonomic nervous system. PP and SP can be improved by combining several normal tests [26] [85] [201] [165] [17] [12] [99] [213].

12


Regardless of the recommended combination of methods, this thesis will be focused on the VLP detection, trying to improve its individual performance by several novel approaches. In the future, it is hoped that these improved techniques to detect VLPs can be combined with other techniques to achieve improved prognosis for many patients at risk of SCD.

1.3 Ventricular Late Potentials (VLPs) VLPs are low-amplitude, broad-band-frequency signals, which appear in the HRECG, associated with the arrhythmogenic substrate in some cardiac diseases.

Therefore,

detection of VLPs can be used as a diagnostic marker. Since these very low level signals are masked by the other components of the ECG and by noise and interference, both in time and frequency domains, its detection remains a challenge. 1.3.1 Origin of VLPs When some region of myocardial (heart muscle) tissue is damaged, conduction delays and blocks can alter the normal electrical activity of the heart. A delayed impulse provokes a late depolarisation after the end of the QRS complex in the ECG signal, which appears as VLPs. ECG and conductive system The waveform resulting from the electrical activity in the conductive system of the heart (Figure 1.4) is called the electrocardiogram, ECG (Figure 1.3). The electrical activity is initiated by depolarisation of the sino-atrial (SA) node, which is the natural pacemaker

13


firing at about 70 times/minute and then, flows through the atria’s fibres to the atrioventricular (AV) node.

Amplitude (µV)

1000

R

500

VLP

P

T

0

Q

S

-500

-1000 0

200

400

600

800

1000

Time (ms)

Figure 1.3 ECG signal (one beat or complex P-QRS-T, healthy 20, Y-lead).

Figure 1.4 Conductive system of the heart.

The horizontal segment preceding the P-wave is the baseline, which is theoretically isoelectric. The P-wave itself represents the atria depolarisation (contraction of the atria) and is followed by a repolarisation action that does not generate a pronounced potential. Some authors refer that this process coincides in time with the ventricles depolarisation

14


and it is obscured by its resultant potential, the QRS complex. The AV conduction time (PQ interval preceding the QRS complex) should allow sufficient time for complete contraction of the atria and hence the ventricles can be filled with blood before following contraction of the ventricles. AV repolarisation is followed by ventricular depolarisation (QRS complex) through the bundle of His. Finally, the repolarisation of the ventricles is associated to the T-wave. Myocardial infarction and tissue damage The myocardium needs its own blood supply to provide the necessary metabolism for muscular contraction. Oxygenated blood is therefore passed from the lungs to supply the cardiac muscle via the coronary arteries. This blood then empties into the right atrium to be passed back through the lungs via the right ventricle. An interruption in this supply to a given region of the myocardium provokes an oxygen deficiency, damaging the tissue within the affected area. If an atheromatous artery (with a deposition of plaques, maybe related to a high level of cholesterol) is blocked by a thrombosis, the down-stream blood flow will be insufficient to maintain a normal cardiac metabolism. This condition is called ischemia. If the reduced blood supply is sufficiently low, then the affected tissue will die after a few hours, resulting in a MI, which is the most common cause of myocardial damage. The post-infarction myocardium forms a scar that is inactive electrically (and mechanically). The scar is surrounded by electrically abnormal myocardium, consisting of normal cells alternating with scar tissues and of chronically ischemic cells that are partially depolarised. This abnormal tissue surrounding the scar is the substrate [152]

15


that supports the VT. Re-entrant circuit Although some other mechanisms (like automaticity and triggered activity, which have to do with abnormal impulse formation [85]) can give rise to VT, in the majority of post-MI cases, a conduction phenomenon termed re-entry is responsible. Anisotropy, which is the differences in fibre conductivity in different directions, and depolarisation dispersion are responsible for the re-entrant circuit propagation. Due to a longer pathway of excitation, or a slower conduction velocity, or both [26], a conduction delay may be originated in the damaged area. A damaged area in the myocardial tissue with conduction delays and blocks results in a non-homogeneous dispersion of the impulse between the normal and the damaged parts, which enables the re-entrant electrical circuit.

delay

Unidirectional block

Figure 1.5 Re-entrant phenomenon in damaged section of myocardium.

Figure 1.5 illustrates this re-entrant phenomenon. If an impulse finds two different paths,

16


it will split and take both; if one path is unidirectionally blocked and the other one is sufficiently delayed, due to tissue damage, to allow recovery of the zone initially blocked, then, a VT can be generated. An impulse is delayed inside the slow conduction path and then re-enters to the near tissue, producing another impulse. Due to the delayed impulse, late depolarisation after the end of the QRS can occur, and fragmented electrical signals can be detected as VLPs at the terminal portion of the high-resolution QRS complex. Abnormal intra-QRS potentials More recently, abnormal intra-QRS potentials have been suggested analogous to conventional VLPs, in the sense that they may be arrhythmogenic [143] [146] [24] [44] [81] [80] [79]. It is hypothesised that these potentials may reflect disruption and/or delay in ventricular conduction that is potentially arrhythmogenic. The concept of VLPs might be expanded to include abnormal potentials occurring anywhere within the period of the QRS complex in the HRECG, rather than only the last segment. 1.3.2 VLPs and cardiac care In clinical cardiology, VLPs are found in between 10% and 50% of all cardiac diseases [36] [161]. On the other hand, more than 93% of patients without VLPs are “healthy” people [26], so detection of VLPs is an important diagnostic marker. Detection of VLPs in the HRECG can be used to: •

detect post-MI patients prone to sVT and SCD,

•

evaluate thrombolytic and coronary angioplasty therapy and anti-arrhythmic drugs after MI,

•

follow progress of patients after anti-tachycardiac surgery, or some other kind of 17


heart surgery, •

judge the evolution of some cardiac conditions: cardiomyopathy [70], ischemia [41] [181] [77], myocarditis [32] [102] [178], angina pectoris [6] [205], congenital heart disease [36] [24],

•

study patients with risk factors for cardiovascular disease: hypercholesterolemia [120], hypertension, diabetes mellitus, smoking, heavy drinking [150], and sports practising.

Some other VLP studies deal with Kawasaki disease, antidepressant therapy, sleep apnea syndromes, muscular dystrophy, chronic dialysis treatment, and HIV [21]. Vulnerability to VT and SCD Most of VLP studies reported are concerned with risk stratification for sVT and SCD in post-MI patients [134] [161] [34] [96] [205] [211] [152] [99] [45] [163] [213]. Results summarised elsewhere [26] [85] [17], show that between 12 and 29% of post-MI patients with VLPs conventionally detected, develop sVT or die suddenly, contrasting with only between 0.8 to 4% of those whose HRECG is normal. The SE of this marker varies from 60 to 91%, and SP, from 57 to 79%, in different studies, although high values of SE and SP at the same time are difficult to achieve, limiting the traditional VLP detection applications. Effects of reperfusion and anti-arrhythmic therapies Most cases of MI occur when atherosclerotic plaque in a coronary vessel breaks away from the wall and attracts platelets. The consequent thrombus compromises blood flow. Tissue necrosis begins within 20 minutes of the occlusion. Immediate treatment with an antithrombolytic drug (like streptokinase) or percutaneous transluminal coronary 18


angioplasty (PTCA) is needed to restore blood flow and maintain myocardial function. Effective reperfusion therapy (mechanic or thrombolytic induced [110]) prevents the development of an arrhythmogenic substrate after MI. Numerous papers dealing with the predictive value of VLPs to evaluate the success of thrombolysis or PTCA after MI have been published [41] [103] [110] [114] [125] [144] [181] [77]. In this sense, VLPs are a better predictive marker than the traditional rate of ectopic activity. The absence of VLPs indicates an enhanced ventricular electric activity; successful thrombolytic therapy seems to reduce VLP incidence. If an anti-arrhythmic therapy is followed after a MI, the evolution of the HRECG can help to evaluate, indirectly, its effectiveness. Studies involving drugs as mexiletine, disopyramide, chinidine, propafenone, sotalol, amiodarone and flecainide have been conducted with VLP analysis. Post-operative patients VLP analysis has been used successfully as a post surgical follow-up technique for patients with congenital heart disease.

These studies include patients with right

ventriculotomy, operation of Rastelli, and operation of Kawashima, extra-cardiac conducts insertion, tetralogy of Fallot, transposition of the great arteries, aortic stenosis, coarctaction of the aorta and ventricular septum defect [24]. The VLPs have also been used in cases of revascularization and coronary artery bypass grafting. More frequently, VLPs have been used as a follow-up methodology for patients after anti-tachycardiac procedures.

Those with VLPs previous to the operation in whom

HRECG returned to normal, are more unlikely to develop VT (only less than 10% of 19


them will suffer from VT) [26] [24] [65]. Finally, analysis of VLPs from HRECG may help in the detection of acute rejection after a cardiac transplant [26]. Other studies Patients with risk factors for cardiovascular diseases as hypertension, diabetes mellitus and smoking can be evaluated by HRECG analysis. VLPs are frequently found to be associated with high blood pressure patients. Some studies suggest that diabetes mellitus patients have intra-ventricular conduction disturbances due to diabetes microangiopathy, which can be detected using VLP tests. People who smoke present a high risk for SCD, but no significant differences in VLP incidence have been found to be associated with habitual smokers compared to those who do not smoke. VLPs are not uncommon in sports players and appear related to the left ventricular hypertrophy. 1.3.3 Characteristics of VLPs. Why are they so difficult to detect? The amplitude and frequency characteristics of VLPs, its small duration, and the position they occupy in the HRECG signal, make its detection very difficult. This, coupled with the fact that these signals are very often corrupted by noise and interference, makes VLP monitoring a very challenging problem. Amplitude characteristics VLPs are very low-amplitude signals. These signals appear in the order of 1 to 20µV in the HRECG while using surface electrodes; that is, they are much smaller than the other components of the HRECG (Figure 1.3).

20

For instance, the QRS complex, which


“precedes” them, has typical amplitude of 1 mV. Not only the other components of the ECG can mask the VLPs.

The noise and

interference corrupting the ECG signal can have amplitudes much higher than the VLPs, causing the SNR in the segment of interest (end of QRS complex) to be less than unity. Noise and interference affecting VLPs Noise and interference (Figure 1.6) affect the ECG signal in general, and more severely the VLPs. These disturbances can be associated with the patient, the electrodes, the cables, and the electronic instrumentation system. The voluntary or involuntary movement of the patient (due to respiration, coughing, shaking, etc.) provokes changes in the electrode/electrolyte interface, and therefore, generates movement artefacts. The effects of the respiration can be manifested as a baseline wandering (Figure 1.6 a) and /or as an amplitude modulation (Figure 1.6 b). Through the cables, undesirable signals can be electrostatically coupled or electromagnetically induced. An example of the undesirable signals is the 60/50Hz powerline interference (Figure 1.6 c). The most appropriate room for VLPs studies would be a Faraday cage, which provides electrostatic screening.

Screening from

magnetic influences is more difficult. As a practical solution, the magnetic induction can be minimised by keeping the patient cables close each other (pick up area small) and locating the room as far away as possible from electromagnetic interference sources (e.g. motors, diathermy equipment, etc.).

21


200 ms

250µV

a) Effects of respiration: baseline wandering (p36, X-lead, 122.8-124.2s). 200ms

250µV

b) Effects of respiration: amplitude modulation (healthy 49, X-lead, 7.5-9.9s).

250µV 200ms

c) 60 Hz powerline interference (p18b, X-lead, 0.4-2.8s). 200ms

500µV

d) EMG noise (p15b, Z-lead, 62.4-65s). Figure 1.6 Noise and interference corrupting the ECG.

22


All the electronic components used in the instrumentation for VLPs detection, especially in the first stages of the instrumentation amplifier, should be very low noise. Using these kinds of expensive low noise components, the noise associated to the instrumentation can be drastically reduced but not totally removed. The presence of the instrumentation noise in the ECG signal has the same appearance as the EMG noise. The compound noise corrupting the ECG can be seen as a broadband frequency signal, overlapping with the frequency components of VLPs. Besides, its amplitude normally far exceeds that for the VLPs, leading to a very poor SNR. Position of the VLPs in the HRECG Conventional studies of VLPs assume that they are restricted to the last segment of the QRS complex, and initial part of the ST segment, as it was shown in Figure 1.3. More recent theories consider VLPs as a subset of the abnormal intra-QRS signals (notches and slurs) [146] [24] [44] [81] [80] [79]. These theories consider that the areas involved in the VT circuit are mostly activated during the QRS complex and not only in the early ST segment. Therefore, it is necessary to examine a larger portion of the QRS complex to be able to distinguish more precisely arrhythmogenic areas of the myocardium, with the hope that predictability of these tests will improve. Unfortunately, the QRS complex masks considerably these intra-QRS waveforms. Frequency characteristics Traditionally, VLPs have been considered as high frequency signals. Actually, VLPs include components at much higher frequencies than the rest of the waveforms in the conventional ECG. The ECG elements are usually restricted from 0.05 to 100Hz [57],

23


and the most significant spectral components are confined at a smaller range, as it is shown in Figure 1.7. On the other hand, VLPs can carry information even at frequencies of 250 Hz to 300Hz [26]. This suggests the idea that VLPs could be “isolated” from the host ECG by using a high pass filter [182]. Unfortunately, some of the VLP frequency components (around 25 to 40Hz [26], or lower) overlap with those of the conventional ECG. Consequently, using a high pass filter to isolate VLPs from the rest of the ECG is just a compromise. Normalised PSD 1

ECG 0.8 0.6

QRS 0.4 0.2

P-T 0 0

5

10

15

20

25

30

35

40

Frequency (Hz)

Figure 1.7 Power spectral density of the ECG, QRS complex and P and T waves.

Difficulties to isolate VLPs Along with the negative SNR in the segment of interest, and frequency overlapping of VLPs with the other components of the ECG, noise and interference, there are some other practical limitations to the isolation of VLPs. The fast transition at the end of the QRS complex preceding the low-amplitude VLP region, is a problem for any filtering technique because some degree of ringing can appear in the VLP region. In such cases, this ringing can be interpreted as the presence of VLPs, even when they are not present in the original signal (increasing FPs), or they can mask VLPs when present (increasing

24


FNs). In addition, the HRECG is highly non-stationary, affecting the performance of adaptive filtering and other conventional filtering techniques.

1.4 Objectives The purpose of this investigation is to develop a reliable, non-invasive, efficient system to detect VLP signals in order to generate cardiac diagnostic markers. Current techniques for detection of VLPs, in general, pose the following limitations: •

Averaging of a significant number of beats is required.

•

Inability to operate properly with non-stationary data.

•

Inability to obtain specific beat-to-beat variability information.

•

Analysis constrained to the end of the QRS complex.

•

Poor SE and SP in VLP detection (Section 1.2.3).

This work proposes to develop ECG pre-processing and processing algorithms for detection of VLPs to improve upon current sensitivity and specificity bounds, and to reduce the number of required beats. The global objective of this research is to improve VLP detection, while designing computationally affordable algorithms that can be efficiently implemented in computerbased HRECG analysers. As VLP detection represents a prominent non-invasive marker for cardiac and cardiac related diseases, an improved method to detect VLPs will allow for better diagnosis capabilities. Therefore, the expected results of this work will have a direct impact on many areas of the health care system, and on the lives of many individuals.

25


It should be understood that this work is concerned with the detection problem and is not concerned with the actual measurement of VLPs. However, once a reliable detection scheme has been designed, this will lay the foundation for further research into the measurement problem.

1.5 Thesis outline In this first chapter, the motivation for this work has been established. VLP detection has been introduced as a promising method to assess patients at risk for SCD. The characteristics of VLPs have been discussed along with the difficulties that make detection of these signals a very challenging process. The conclusions reached include the fact that the detection of VLPs has to be improved. The objective of this thesis is stated as the design and implementation of novel signal processing techniques to improve the use of VLPs in the management of CVD. The second chapter consists a literature review on the topic of VLP research, highlighting the current clinical and research approaches. This review includes what has been published dealing with the instrumentation requirements to acquire the VLPs and the digital signal processing algorithms used to enhance the SNR for detection. The characteristics, main boundaries, and conflicts of the present techniques are described. The non-stationary nature of ECG signals, and VLPs in particular, naturally leads research to concentrate in the area of multidimensional signal representation and filtering. Chapter three focuses on these new trends.

The characteristics of different

multidimensional time-frequency (t-f) representations, and their application in VLP analysis, are reviewed.

The topics of wavelets and wavelet packets, as special t-f 26


representations, are also introduced. Chapter four describes a flexible PC-based system developed in this thesis to acquire, detect and analyse VLPs.

This system overcomes some of the limitations of the

commercial HRECG systems available today. Characteristics of a HRECG database, collected by using this system and which will be used in the rest of the thesis, is also summarised. Models and simulations of HRECG signals used to test the various new algorithms developed in this work are described. Chapter five includes pre-processing algorithms, especially designed for VLP analysis but with potential applications in general ECG. Among these algorithms, a powerline cancellation technique proved its efficiency associated to VLP detection. In addition, a QRS detector, as well as an FIR filter design evaluated here, showed some advantages compared to those described in the literature. Chapter six deals with specific VLP processing techniques designed in this thesis. The classical time domain analysis was improved by using a modified signal averaging technique and other minor contributions. Another original design combines an adaptive enhancer with the modified signal averaging to obtain certain beat-to-beat information, and improved the overall VLP detection. Finally, a bi-dimensional (2-D) VLP detection scheme using wavelet denoising and edge detection algorithms achieved a better performance than the typical analysis techniques. Conclusions are given in chapter seven. A summary of the topics developed here, as well as original contributions, is included. At the end, recommendations for future work are proposed, based on findings and limitations of this thesis.

27

Chapter 2 - Current clinical and research approaches

Chapter 2 - Current clinical and research approaches 2.1 Introduction Low-level signals, directly recorded from ischemic regions of a canine model of MI, were described for the first time in 1973 [25]. This was followed in 1978 with the first recording of VLPs, again in a canine MI model, using surface electrodes [46]. In the same year, studies on VLPs recorded from the human endocardium were published [104]. In 1981, Simson introduced the basis for non-invasive studies of VLPs in man in the time domain [182], which was adopted as a standard ten years later [26]. During the 1980’s, VLP studies in the frequency domain were essayed [49]. More recently, VLP studies in the time-frequency plane were proposed [121].

Figure 2.1 System for detection and analysis of VLPs.

The detection and analysis of the VLPs require special instrumentation or HRECG acquisition systems, and digital signal processing techniques for the enhancement and analysis of the signal of interest (Figure 2.1). Once the ECG signal is acquired, by using high-resolution equipment, a noise diminishing strategy has to be applied in order to obtain the relevant information associated to the presence (or absence) of the VLPs.

28


2.2 Instrumentation requirements The first stage in any ECG acquisition is the electrode-lead system. This is followed by analog conditioning circuitry that includes differential amplification, common mode rejection and filtering. Analog-to-digital conversion is then performed to provide a signal that is suitable for sophisticated signal processing and computer analysis. Electrodes Electrodes are transducers that convert the ionic currents in the biological system to electronic currents compatible with the electronic instrumentation. The electrograms recorded during invasive EPSs need special internal electrodes that are placed by means of catheters [220] [118] [133] [90] [197]. Some other “non-invasive” VLP studies have successfully used multipolar intra-esophageal electrodes. However, most VLP recording systems use surface electrodes placed on the skin. The surface electrodes of choice for VLP studies are silver/silver chloride (Ag/AgCl) [26], which are non-polarizable, low-noise, very stable, and provide a low half-cell potential. Good skin preparation, including cleansing and abrasion, is needed before placing the electrodes. In addition, the use of an electrolytic paste will help to reduce the contact impedance. Published standards [26] state that “ideally, electrode impedance should be measured and be less than 1000 Ω.” However, it is not clear if they refer to the contact impedance or to the overall electrode/skin impedance. In addition, the frequency at which impedance should be measured is not mentioned.

29


Lead systems Amplitude, polarity, and even duration of the ECG components depend on the position of the electrodes on the body. Therefore, these characteristics depend on the lead system used. The most common ECG leads are reviewed in Figure 2.2. This standard 12-lead system includes three basic bipolar leads (D1, D2, and D3), three unipolar augmented leads (aVR, aVL, and aVF), and six pre-cordials or chest leads (V1 to V6). This system has been used for VLP detection [115] but not very often.

L

+

+

L

+

R R

D1

D3

D2 F

a) D 1= L - R

L

F

+

L

R

L

+

R

F

F

L

L+F 2

e) aVL = L −

+

R+F 2

V1: V2: V3: V4: V5: V6:

V

V 1~6 V1 V2 V3 V4 V5 V6

F

g ) V 1~ 6 = V −

aVF

aVL

F

d) aVR = R −

+

R

aVR

R

c) D 3= F - L

b ) D 2= F - R

R + L + F 3

f) aVF = F − L + R

2

4th intercostal space, at right margin of sternum. 4th intercostal space, at left margin of sternum. midway between V2 and V4. 5th intercostal space, at midclavicular line. same level as V4, at anterior axillary line. same level as V4, at midaxillary line.

Figure 2.2 12-lead system commonly used in clinical ECG.

30


When a tri-dimensional representation of the ECG is required, as in the case of VLP studies, an orthogonal system is normally preferred. The standardised lead system for VLP studies [26] is the orthogonal bipolar XYZ system [182] shown in Figure 2.3.

Figure 2.3 XYZ orthogonal lead system recommended for VLP studies.

The electrodes for the X-lead are placed at the fourth intercostal space in both midaxilary lines (the left electrode is connected to the non-inverting input of the amplifier). The Ylead takes the potential between the left iliac crest (non-inverting electrode) and the intersection of the first intercostal space with the left midclavicular line. The Z-lead is measured between the chest and the back, placing the non-inverting electrode at the fourth intercostal space at left margin of sternum, and the inverting one, on the reflection of the non-inverting on the back. In most of the VLP studies, the filtered leads are combined to form a cardiac vector magnitude [26],

V = X 2 +Y 2 + Z2 ,

31

Eq. 2.1


as a sub-optimal method of data reduction [33].

In order to obtain computational

simplicity, the sum of the absolute values has been used in some studies [33] [98], S= X +Y +Z .

Eq. 2.2

The frequency content in ECG signals depends on the lead used. Established criteria using a lead system cannot be applied to others. However, quasi-equivalent systems have been found. For example, modified orthogonal systems, precordial leads V4, V6 and V2, and individual orthogonal leads (X, Y and Z) [33] [193] may improve the sensitivity to detect ventricular arrhythmia due to better SNR compared to the vector magnitude V. To evaluate spatial localisation of VLPs and noise, systems using multiple unipolar thoracic leads, have been developed [33] [64]. Amplification The first stage in the ECG amplifier should be a differential one with a high gain (Ad) and a high common-mode rejection ratio (CMRR) [142].

In a conventional

electrocardiograph, the gain is typically 1 000, but it may be even higher in a HRECG system. To obtain a high value of Ad, several amplifier stages are needed. The first stage should have a gain (A1) as high as possible (without saturation), and it should be very low noise (N1→0) in order to minimise the total level of the instrumentation noise referred to the input (Ns). The total noise Ns can be expressed as a function of the gains Ai and the individual noise Ni of every i-th stage [54]. In the case of 3 stages,

Ns =

N 1 A1 A2 A3 + N 2 A2 A3 + N 3 A3 . A1 A2 A3

32

Eq. 2.3


Ns can be measured by shorting the inputs of the first stage and should be 114ms, LASd > 38ms, and RMS40 < 20µV. Balance between sensitivity SE and specificity SP (Section 1.2.3) can be controlled by selecting one, two or three of above three criteria at the same time [216]. Figure 2.11 shows an

53


example of a patient with the three time-domain criteria reached, although QRSd and LASd are very close to the thresholds mentioned above. From the LASd and RMS40 parameters, some morphology information can be extracted indirectly, but signal morphology around the terminal part of QRS includes a significantly larger amount of information. To extract more information, artificial neural networks (ANN) have been used in recent works [92] [112] [216] [167] [89] [117] [214], achieving better SE and SP in time-domain VLP analysis. To detect and analyse VLPs, fractal dimension analysis has also been used. In these studies, Escalona and collaborators [72] [132] have used the fractal dimension of the VLP attractor (3-D VLP geometric curve) to quantify the degree of complexity of VLPs in the time domain. Time-domain analysis can isolate the VLPs in the ECG signal. It provides less false positives (FPs) than other methods, it has the best reproducibility [31] [209] and its basic guidelines are standardised [26].

Nevertheless, the noise level and the number of

averaged beats affect time-domain analysis definition and high-pass filters can introduce artificial signals, which affect the final results. Furthermore, this approach cannot be implemented on patients with bundle branch block.

These limitations warrant the

development of other approaches. 2.4.2 Frequency domain

Parallel to the time-domain, frequency-domain techniques for VLP analysis have been established. Most studies in the frequency domain are based on Fourier transformation and the periodogram, although some researchers have used the Fast Harley Transform

54


[32], maximum entropy spectrum estimation [179] [210], time variant auto-regressive spectral analysis [39], spectral turbulence analysis [134] [84] [209] and acceleration spectrum analysis [208] [209]. In the frequency domain, stationary signals can be described by means of the amplitude (|X(f)|) and phase (θ(f)) of the sine waves in which they can be decomposed. To obtain the equivalent frequency domain representation X(f) of a signal, given its description in the time domain x(t), the Fourier transform (F{⋅}) is used (Eq. 2.22). Inversely, the inverse Fourier transform (F-1{⋅}) transforms a signal from the frequency domain into the time domain (Eq. 2.23).

X ( f ) = F {x(t )} =

∞

∫ x(t )e

− j 2 πft

dt = X ( f )e jθ( f )

Eq. 2.21

−∞

x(t ) = F

−1

∞

{X ( f )} = ∫ X ( f )e j 2πft df

Eq. 2.22

−∞

A useful tool for VLP spectral analysis is the power spectral density (PSD). This parameter gives the density of power on the frequency axis. The PSD of the signal x (Φxx) is defined as the Fourier transform of the autocorrelation function (φxx).

Φ xx ( f ) = F {φ xx } =

∞

∫ φ (k )e

− j 2 πft

xx

dt

Eq. 2.23

−∞

φ xx (m ) = E [x(i − m )x(i )]

Eq. 2.24

For sampled signals x[m] (with sampling frequency fs and M samples), the representation in the frequency domain X[k] can be obtained by using the discrete Fourier transform

55


(DFT), efficiently calculated by means of the Fast Fourier Transform (FFT) algorithm in most implementations [145]. It should be noticed that the spectrum of the sampled signal is the spectrum of the original signal repeated at every multiple of the sample frequency fs. The inverse operator, IDFT, transforms the sequence X[k] back into the time domain x[m]. X [k ] = DFT {x[m]} =

M −1

∑ x[m]e

− jkm

Eq. 2.25

m =0

x[m] = IDFT {X [k ]} =

1 M

M −1

∑ X [k ]e

jkm

Eq. 2.26

k =0

The autocorrelation can be estimated by

1 φˆ xx [m] = M

M − i −1

∑ x[m + i]x[i] .

Eq. 2.27

n =0

The frequency resolution ∆f that can be provided by the DFT of an M-sample signal, sampled at a frequency fs is given by,

∆f =

fs . M

Eq. 2.28

The number of samples M of the signal x mostly depends on the segment of interest. The starting point and the length of the window also constitute polemic issues in the literature [23]. The analysis period has been extended towards the T wave, covering the ST segment to improve the frequency resolution of the FFT. The starting point of the interval to be investigated can be determined by using a single threshold in the timedomain signal (e.g. 40µV) or the derivative of it (e.g. 5mV/s) [23] [189].

56


The PSD cannot be calculated from a finite (M-sample) sequence. However, it can be estimated, with certain degree of success, by using several methods described in the literature [87] and reviewed in Figure 2.12. The most common used PSD estimators are based on the FFT because of the efficient implementation and easy applicability associated. One of these FFT-based estimators is the Blackman-Tuckey method [53], which estimates PSD directly from its definition (Eq. 2.24) but using finite integration time and an estimate correlation function.

Another example is the periodogram

estimator, which does not need to estimate the autocorrelation, and the estimated PSD is given by ) f 2 Φ xx ( f ) = s DFT {x[m]} . M

Non-parametric methods

PSD estimation Parametric methods

• Periodogram-based methods (BlackmanTuckey, periodogram, Welch) • Multiple window methods (Slepian sequences)

• Model identification methods (AR, MA, ARMA) • Minimum variance distortionless response method • Eigendecomposition-based methods (PMUSIC)

Figure 2.12 PSD estimation methods described in the literature.

57

Eq. 2.29


In the estimators mentioned above, the data outside the analysis segment is assumed to be zero. This assumption can be seen as a rectangular windowing of the data and it has associated a very high spectral leakage because the initial and final data points of the segment of interest are not isopotential [47]. This spectral leakage can be seen as the occurrence of non-zero DFT values at bin frequencies where no actual spectral components exist in the signal [100]. To overcome this leakage at expense of reduction in the frequency resolution, a different window, which smoothly forces the border samples of the segment of interest to zero, should be used.

The four-term Blackman-Harris window has been the one most

commonly used in the spectral analysis of the ECG [26] [47] although there is no agreement about the type of window that performs the best in VLP frequency-domain analysis. It should be noted that multiplication of the data sequence by the window function in the time domain is equivalent to convolving the FFT of the signal with the FFT of the window. Another way to try to reduce the variance of the estimated PSD, sacrificing resolution, is based on averaging multiple PSDs obtained for shorter data segments. This technique is combined with windowing in the Welch’s averaged periodogram method [100]. Welch’s approach divides the data record into shorter overlapping segments and windows them. Then, the periodogram of every individual windowed segment is computed. Finally, the overall PSD is estimated as the average periodogram. Figure 2.13 compares the implicit 150ms rectangular window and the four-term Blackman-Harris window of the same length. The rectangular window accomplishes the

58


best frequency resolution (~6.7Hz according to Eq. 2.29) because its main lobe in the frequency domain is the narrowest possible [145]. However, this simple window has the worst spectral leakage (bias) due to its significant sidelobes.

The Blackman-Harris

window is a good compromise between bias and resolution (13Hz at –3dB [47]); it has peak sidelobes of –57dB and a rolloff rate of 18dB/octave. Therefore, the BlackmanHarris window can be used to detect small signals in the presence of large signals with

Rectangular

certain degree of success.

Figure 2.13 Implicit rectangular window and Blackman-Harris window (fs=1kHz).

The spectral waveform varies considerably from one study to another, so it is difficult to obtain indexes that quantitatively describe the phenomenon.

Many researchers use

spectral area ratios to quantify the proportion between high and low frequency components in the late QRS [78], or the relative contributions of frequency bands [47]. Other parameters have also been considered [23], but there is not a standard method for frequency-domain analysis. 59


A typical frequency domain analysis technique [49] [47] calculates the relative contribution of the frequency components between 20Hz and 50Hz to the power spectrum, as shown in Figure 2.14. A 150-ms windowed version of the HRECG, by using a four-term Blackman-Harris window, is the segment analysed. The analysis window starts 40ms before the offset of the QRS complex and it expands to the ST segment, trying to obtain a higher resolution. However, the spectral resolution assumed to calculate the integral of amplitudes between 20Hz and 50Hz is greater than the one actually present [122]. In addition, VLP duration is much less than the analysis window length; therefore, these abnormal signals are under represented in the power spectrum [122].

Figure 2.14 Typical VLP frequency domain analysis (X-lead, p18).

60


Frequency-domain implementations achieve good differentiation between signal and noise; they do not need high-pass filtering and can be applied to patients with bundle branch block. Nevertheless, these techniques are limited by their dependence on window functions, which introduces pseudo peaks due to finite data length [145]. Furthermore, results of these tests have a high variability [209] and they lose VLP localisation. This approach has been declared invalid, given the highly non-stationary nature of the HRECG [122]. In an effort to improve VLP detection as a diagnostic marker, some researchers have combined time and frequency analyses [83] [27]. They claim that SE is improved without reducing SP.

2.5 Summary Detection/analysis of VLPs demands a low-noise acquisition unit, which converts the HRECG data to digital format with a sample frequency of at least 1kHz and a resolution of at least 2.5µV. After this stage, certain digital processing algorithms are used to enhance the signal in the segment of interest, that is, to diminish the noise variance while preserving the characteristics of the VLPs. This challenge has been faced by using different strategies ranging from simple coherent averaging, optimal filtering and adaptive filtering, to the more recent techniques of denoising in the wavelet and wavelet packet domains.

All these techniques have limitations but the latter has shown

considerable promise in the enhancement of biological signals, and it will be treated in more detail in Chapter 3.

61


Once the SNR has been improved, the information contained in the HRECG signal can be analysed in the time or frequency domain, which are the traditional approaches. Both of these have several drawbacks that can be circumvented by using a multiple dimension representation such as time-frequency and wavelets. This novel approach will be detailed in Chapter 3.

62

Chapter 3 - Multidimensional representations in VLP studies

Chapter 3 - Multi-dimensional representations in VLP studies As seen in Chapter 2, the VLP time domain analysis shows certain constraints that frequency domain analysis has tried to overcome. The conventional frequency domain techniques, however, are not well suited for VLP analysis because the frequency spectrum of the HRECG varies rapidly with time. Both analyses, in the time and in the frequency domain, are based on mono-dimensional (1-D) representations that provide limited amount of information.

A multi-dimensional, normally bi-dimensional (2-D),

representation of the HRECG may offer a better characterization of the signal. This leads to the use of joint time-frequency representations (TFRs) [183] [184] [198] [158]. In this Chapter, the main concepts of time-frequency analysis are introduced, supported whenever possible by examples in the specific field of the HRECG. In addition, signal enhancement, denoising, and detection techniques based on the t-f plane are explained.

3.1 First attempts In 1988, the first attempts to describe the HRECG in the time-frequency (t-f) plane were done. Lander et al. introduced the idea of spectro-temporal mapping (STM) [121]. The group at the Ludwig Maximilians University (LMU) is also among the pioneers of the STM of the HRECG maintaining their research up to recent years [91] [179] [180] [196] [181]. Both groups, Lander et al. and LMU, conceived the STM of the HRECG by dividing the last portion of the QRS and the ST segment into a certain number of shorter overlapped sub-segments, and estimating the PSD of each of them, as illustrated in Figure 3.1. The

63


position of the segment to be analysed, the number of sub-segments into which it is divided, the length of the segments and its overlapping step, as well as the method used to obtain the frequency components, vary from one research to another, so results are difficult to interpret.

Figure 3.1 STM of the X-lead (fv03) by following the procedure described in [91].

3.2 Pre-processing for VLP time-frequency analysis Frequently, the low-amplitude intra-QRS waveforms (including VLPs) on the HRECG signal need to be emphasised before performing the t-f analysis. Conventional high pass filtering is usually avoided because of the distortion that this may introduce. Instead, the t-f analysis is normally performed on a difference signal obtained by subtracting a smoothed signal from the original one.

64


The LMU group computed the difference spectra of the HRECG [179] based on the difference of the outputs of the maximum entropy method estimated with an “optimal” order and a low order. The optimal-order estimation yields a spectrum with low and high frequency components, while a low-order estimation yields just the low-frequency components of the HRECG. This difference spectra method makes the VLP components more prominent compared with the ascending ST wave, without introducing appreciable distortion. However, because of the subtraction process, the resultant spectra may include negative values in certain segments, which makes interpretation difficult. Several researchers have used interpolation methods to obtain a smoothed version of the HRECG and then subtracted this from the original signal. The difference signal, here in the time domain, is the one analysed by the selected t-f method. It should be noted that not only the VLP components are emphasised, but also any other intra-QRS waveforms. These intra-QRS potentials may provide more information for risk stratification. Bianchi et al. applied an interpolation with a Tchebytcheff polynomial of order 25 [39]. Kestler et al. used a cubic-spline interpolation [112], and Dickhaus and Heinrich a Bezier-spline method [61]. Lichorwic et al. obtained the smoothed signal by simply low-pass filtering the original signal with a 5-sample moving average [128]. Other groups have used system modelling of the HRECG to obtain the smoothed or predictable signal. The residual signal from the model is then analysed in the t-f plane. Parametric linear and non-linear models have been used [81] [80] [122] [123]. Most of these studies have been orientated to the abnormal intra-QRS potentials, but can also be applied to the VLP case.

65


3.3 Desirable properties of the time-frequency representations Before discussing the characteristics of the most popular TFRs used in HRECG studies, it is convenient to review the properties that an “ideal” TFR should satisfy. Therefore, in this section, the desirable characteristics of TFRs are introduced.

To help this

introduction, these properties are divided into five different categories: covariance, statistical, signal analysis, localization, and inner products [38].

In all cases, Tx(t,f)

represents the TFR of the signal designated as x(t), in the time domain, and X(f) in the frequency domain. Covariance properties The covariance properties of the TFRs are associated with the preservation of certain mathematical operations on the signal. An ideal TFR is expected to be: •

frequency-shift (translation in the frequency axis) covariant: T y ( t , f ) = Tx ( t , f − f o )

•

y ( t ) = x ( t ) e j 2 πf o t ,

Eq. 3.1

time-shift (translation in the time axis) covariant: T y ( t , f ) = T x ( t − to , f )

•

for

for

y ( t ) = x ( t − to ) ,

Eq. 3.2

y (t ) =

Eq. 3.3

scale (dilation/compression) covariant: T y (t , f ) = Tx ( at , f / a )

for

a x ( at ) .

For certain applications, the TFR should also satisfy the hyperbolic time shift covariance, convolution covariance and modulation covariance.

66


Statistical properties The statistical properties of the TFRs, Tx(to,fo), are intended to allow measures of the local signal energy in the t-f plane, i.e. the probability that a signal contains a component of frequency fo at time to. These energy-distribution TFRs [19] should be: •

real valued: Tx * (t , f ) = Tx (t , f ) ,

•

Eq. 3.4

non-negative [75] valued: Tx (t , f ) ≥ 0 .

Eq. 3.5

If the t-f energy density is integrated along one variable (t or f), then the energy density corresponding to the other variable (f or t) is obtained. These are the marginal properties, •

time marginal: ∞

m f (t ) =

∫ Tx (t, f )df

2

= x (t ) ,

Eq. 3.6

−∞

•

frequency marginal: ∞

mt ( f ) =

∫ Tx (t, f )dt =

2

X( f ) .

Eq. 3.7

−∞

In addition, these TFRs should preserve the signal energy, mean, variance, and other higher-order moments of the instantaneous signal energy and PSD [38].

67


Signal analysis properties From the signal-processing point of view, it is useful that the TFRs have the same duration and bandwidth as the analysed signal. That is, the TFRs should be: •

finite time supported: Tx (t , f ) = 0

•

for

t > T , if

x(t ) = 0

f > F , if

X(f ) =0

for

t >T ,

Eq. 3.8

finite frequency supported: Tx (t , f ) = 0

for

for

f > F . Eq. 3.9

It is also desirable to characterise the average frequency, at any instant of time, by the instantaneous frequency fx(t), as well as the group delay τx(f) should characterise the average or centre of gravity in the time direction. These terms are defined as: •

instantaneous frequency: ∞

∫ fTx (t, f )df

f x (t ) = − ∞ ∞

∫ Tx (t, f )df

d = 1 arg{x (t )}, 2 π dt

Eq. 3.10

d =− 1 arg{X ( f )}. 2 π dt

Eq. 3.11

−∞

•

group delay: ∞

∫ tTx (t, f )dt

τ x ( f ) = −∞ ∞

∫ Tx (t, f )dt

−∞

68


The instantaneous frequency and the group delay are acceptable descriptors of the t-f characteristics of mono-component signals, but, unfortunately, they are unsuitable for multi-component and noisy signals [5], such as the HRECG. Localization properties The localization properties of the TFR are desirable for high-resolution capabilities. In the case of the HRECG signal, it is important that if a signal is perfectly concentrated in the time domain (an impulse) or in the frequency domain (a sinusoid), then its TFR should be perfectly concentrated at the same time or frequency. This can be expressed as •

time localization: T x ( t , f ) = δ( t − t o )

•

for

x (t ) = δ(t − to ) ,

Eq. 3.12

frequency localization: Tx (t , f ) = δ( f − f o )

for

X ( f ) = δ( f − f o ) .

Eq. 3.13

Inner products property Finally, the TFR should preserve the normal projections, inner products, and orthonormal signal basis functions. This is expressed by the Moyal’s formula or unitary property as

∞ ∞

∫ ∫ Tx (t, f )T y * (t, f )dtdf

−∞ −∞

∞

=

∫ x(t ) y * (t )dt

2

.

Eq. 3.14

−∞

This property is highly desirable in applications such as signal detection and reconstruction (synthesis).

69


3.4 Classification of time-frequency analysis techniques Non-stationary signals, like the HRECG, can be characterised by time varying models and time-frequency distributions (TFDs). The first technique consists of segmenting the data and obtaining a model for every short-time (assumed stationary) segment. The segments should be long enough to achieve accurate estimates of the model parameters, but short enough to keep such parameters stationary over the estimation period; the variations with time occur between segments. The parametric methods most frequently used are those based on auto-regressive (AR) or auto-regressive moving-average (ARMA) models, although the multiple signal classification (MUSIC) method [16] is another alternative. The TFDs, on the other hand, are generally based on the Fourier or the Wavelet transform, and can be divided into linear and bilinear representations.

Another non-parametric

method is based on multiple windows or slepian sequences. 3.4.1 Time-varying models Auto regressive models The time varying auto regressive (AR) model [124] of a discrete signal x is given by M

x[k ] = ∑ a m,k x[k − m] + ε [k ] ,

Eq. 3.15

m =1

where M is the order of the AR model, am,k (m = 1,…, M) are the weight coefficients, and

ε is the modelling error. Assuming that ε is a white noise process with variance σn2, the TFR of a segment centred at time k can be estimated as,

70


σ 2n

Φ xx (k , f ) =

M

1 + ∑ a m,n e − j 2 πfm

2

.

Eq. 3.16

m =1

The LMU group proposed a version of the STM of the HRECG based on the maximum entropy method (Burg algorithm) [179]. They used 35 overlapping segments of 40ms, with the first one starting 32ms after the offset of the QRS and the last one starting 36ms before the same reference (step of 2ms). Other groups have used different variants of AR models for t-f analysis of the HRECG [39]. The results of these studies are a consequence of the pros and cons of the AR-based TFRs. In general, the AR modelling allows a good frequency resolution even with short data sets. However, for a highly non-stationary signal such as the HRECG, which has no harmonic structure, this method is not able to provide a high degree of frequency resolution and perform a significant principal decomposition. Lander and Berbari [122] suggested that the resolution reached by the AR method in the HRECG analysis is no better than that obtained by the spectrogram (Section 3.4.3). In addition, the choice of the model order may be critical because the conventional methods to estimate it do not apply for the HRECG [179]. Low model orders are associated with an over-smoothed STM, while high-orders introduce spurious details in the spectra, which may affect the interpretation of the HRECG. In addition, AR modelling is less stable and more susceptible to noise [124] than the other methods for t-f analysis. Auto-regressive moving-average models

Adaptive spectral analysis [124] is another model-based t-f analysis method. In this case, the power spectrum of the signal is calculated from the auto-regressive moving-average

71


(ARMA) parameters. This should yield an increased spectral and temporal resolution over AR. Unfortunately, this ARMA modelling involves non-linear equations that affect the relative amplitudes of multi-component signals, like those in the HRECG. 3.4.2 Linear time-frequency distributions Short-Time Fourier Transform

An intuitive way of solving the limitations of the Fourier transform (FT) for analysis of non-stationary signals consists of pre-windowing such a signal into shorter quasistationary subsets and then, calculating the FT of every window segment.

This is,

precisely, the short-time Fourier transform (STFT), which is the simplest of the linear TFDs also known as atomic decompositions. The STFT of a signal can be formulated as,

STFTx (t , f ; w) =

∞

∞

−∞

−∞

* * j 2π( f − f )t − j 2 πfτ df ' , Eq. 3.17 ∫ x(τ)w (τ − t )e dτ = ∫ X ( f ' )W ( f '− f )e

where x(t) is the input signal in the time domain, X(f) is its equivalent representation in the frequency domain, and w(t) is the short-time analysis window around t=0 and f=0 (W(f) is its version in the frequency domain). The STFT can be thought of as a local spectrum of the signal x(τ) around t, or the result of passing the signal x(τ) through a band-pass filter whose frequency response is W*(f’-f). That is, the STFT is similar to a bank of band-pass filters with constant bandwidth [5], and therefore, with constant frequency resolution, which is proportional to the effective bandwidth of analysis window w. For a sampled signal x[n], the STFT can be efficiently implemented by using the FFT algorithm as

72


STFTx [n, m; w] = ∑ x[k ]w * [k − n ]e − j 2 πmk ,

−

k

1 1 ≤m≤ , 2 2

Eq. 3.18

where k is the step with which w is displaced to window the data, and it must be a multiple of the sampling period. In general, the atoms wn,m constitute a discrete over-sampled set of non-orthonormal elements (frame). It should be noted that it is impossible to obtain an orthonormal basis with a window w that is both well localized in time and frequency (Balian-Low obstruction theorem [59]). Time-frequency resolution

As for any other linear TFD, there is a trade-off between time and frequency resolution of the STFT, given the Heisenberg-Gabor inequality, which refers to the low-bounded timebandwidth product TB [5].

TB ≥ 1 ,

Eq. 3.19

where, ∞

4 π ∫ (t − tm ) w(t ) dt T=

2

−∞

∞

∫ w(t )

2

dt

−∞

.

∞

4 π ∫ ( f − f m ) W ( f ) df B=

−∞

2

∞

∫ w(t )

−∞

and,

73

2

dt

Eq. 3.20

Chapter 3 - Multidimensional representations in VLP studies ∞

∫ t w( t )

2

dt

tm = − ∞ ∞

∫ w(t )

2

dt

−∞ ∞

.

∫ f W( f )

2

Eq. 3.21

df

fm = −∞

∞

∫ w( t )

2

dt

−∞

If w(t )

2

is considered as a probability density function, tm can be interpreted as its mean

value, i.e. the average time, and T 2 as its variance σt2, which represents the spreading in the time direction of the window w. With similar reasoning, but in the frequency domain, fm can be seen as the average frequency and B2 as the frequency spreading σf2. The lower bound, TB=1, is reached for Gaussian functions, although in the case of discrete implementations, they may not provide the most compact basis [67] [68]. Another typical linear TFR is the Wavelet Transform (WT), which is detailed in Section 3.6. 3.4.3 Bilinear time-frequency distributions

The linear TFDs described in the previous section are relatively easy to compute and interpret. However, they do not reveal, directly, the energy structure of the signal, which may help in most analyses. Since the energy is a quadratic function of the signal, a quadratic TFD should distribute the energy of the signal evenly over both time and frequency (or scale) domains.

74


Spectrogram and scalogram

Following this reasoning, the spectrogram, which is the squared modulus of the STFT, can be interpreted as the measure of the energy signal contained in the t-f domain, centred on the point (t,f). A similar distribution is the scalogram, defined as the squared modulus of the continuous WT (Section 3.6), which is an energy distribution of the signal in the timescale plane. The spectrogram and the scalogram are just two of the most popular energy distributions, also called quadratic or bilinear TFDs. They have been used in numerous studies of the HRECG signal, some of them comparing their performances [107] [140] [61] [174]. Wigner distribution

Another important bilinear TFD is the Wigner distribution (WD), defined as ∞

∞

ν⎞ ν⎞ ⎛ τ⎞ ⎛ τ⎞ ⎛ ⎛ WDx (t , f ) = ∫ x⎜ t + ⎟ x * ⎜ t − ⎟e − j 2 πfτ dτ = ∫ X ⎜ f + ⎟ X * ⎜ f − ⎟e − j 2 πfν dν . 2⎠ ⎝ 2⎠ 2⎠ 2⎠ ⎝ −∞ ⎝ −∞ ⎝

Eq. 3.22

The WD has been extensively used in HRECG studies [212] [61] because it yields high t-f concentration, while preserving the t-f marginals (Eqs. 3.6 and 3.7). Actually, the WD satisfies most of the desirable properties of the TFRs (Section 3.3). However, the nonlinear nature of this quadratic TFD yields interference or cross-terms, i.e. components that are not present in the original signal. These may mask the auto-terms, i.e. the components in the original signal, and make the interpretation of the signals difficult. Cross-terms in the bilinear TFDs

Every bilinear TFD applied to multi-component signals yields cross-terms at a certain level. For instance, the WD of a sum of two mono-component signals x(t)+y(t) is given by

75


{

}

WD x + y (t , f ) = WD x (t , f ) + WD y (t , f ) + 2 Re WD x , y (t , f ) ,

where the last term represents the interference.

Eq. 3.23

Here, the cross-Wigner distribution

WDx,y(t,f) is defined as ∞

WD x, y (t , f ) =

⎛ x⎜ t + ⎝ −∞

∫

τ⎞ ⎛ τ ⎞ − 2 πfτ dτ . ⎟ y *⎜ t − ⎟e 2⎠ ⎝ 2⎠

Eq. 3.24

The cross-terms are oscillatory and may overlap with the auto-terms. To reduce the number of cross-terms generated between the positive and negative frequency components, the analytic signal is used2. This analytic signal xa(t) is constructed from the original signal x(t) via the Hilbert transform HT, xa (t ) = x (t ) + jHT {x (t )}.

Eq. 3.25

this can be represented as a folding in the frequency domain, ⎧2 X ( f ), f > 0 ⎪ X a ( f ) = ⎨ X ( f ), f = 0 . ⎪0, f < 0 ⎩

Eq. 3.26

The oscillations of relatively high frequency of the remaining cross-terms can be smoothed at the expense of auto-component broadening, distortion and loss of desirable TFR properties. As an example of this technique, the pseudo-Wigner distribution (PWD) uses a moving window in the time domain that introduces a convolution in the frequency direction, ∞

PWD x (t , f ) =

2

τ⎞ ⎛ τ⎞ ⎛ x ⎜ t + ⎟x * ⎜ t − ⎟ w( τ)e − 2 πfτ dτ . ⎝ 2⎠ ⎝ 2⎠ −∞

∫

The WD of the analytic signal is often called the Wigner-Ville distribution (WVD).

76

Eq. 3.27


By windowing, the PWD also enables numerical computation by limiting the length of the signal. Another TFD, the smoothed WD (SWD), convolves a 2-D filter F(t,f) with the WD of the signal, thus reducing cross-terms with oscillations in both directions of the t-f plane [185] [215]. More recently, a method to remove cross-terms from the WD by nonlinear filtering was presented [8]. The Cohen class of TFDs

All bilinear TFDs that satisfy Eq. 3.1 and Eq. 3.2, i.e. translation covariant in the time and frequency axis, are grouped in the Cohen class or shift-covariant class. Every TFR, Tx(t,f), of this group can be obtained by convolving a t-f-dependent kernel, ψc(t,f), with the WD of the signal, and therefore, they can be considered as smoothed versions of the WD, ∞ ∞

Tx (t , f ) =

∫ ∫ψ

c

(t − t ' , f − f ' )WD x (t ' , f ' )dt ' df ' .

Eq. 3.28

− ∞− ∞

The Cohen class of TFDs can be also expressed as a function of the time domain signal x(t) and the kernel ϕc(t,τ), or the frequency domain representation X(f) and the kernel Φc(f,ν), or the ambiguity function3 AFx(τ,ν) and the kernel Ψc(τ,ν). ∞ ∞

Tx (t , f ) =

⎛

τ⎞

⎛

τ⎞

∫ ∫ ϕ (t − t ' , τ) x⎜⎝ t '+ 2 ⎟⎠ x * ⎜⎝ t '− 2 ⎟⎠e c

− j 2 πfτ

dt ' dτ

− ∞− ∞ ∞ ∞

=

∫ ∫Φ

c

−∞−∞

ν⎞ ν⎞ ⎛ ⎛ ( f − f ' , ν) X ⎜ f '+ ⎟ X * ⎜ f '− ⎟e − j 2 πfτ df ' dν , 2⎠ 2⎠ ⎝ ⎝

∞ ∞

=

∫ ∫ Ψ (τ, ν) AF (τ, ν)e c

x

−∞−∞

where,

3

2-D Fourier Transform of the Wigner Distribution.

77

j 2 π ( tν − fτ )

dτdν

Eq. 3.29

Chapter 3 - Multidimensional representations in VLP studies ∞ ∞

ϕ c (t , τ) =

∫ ∫Φ

c

( f , ν )e

j 2 π ( fτ + νt )

− ∞− ∞

dfdν = ∫ Ψc (τ, ν)e j 2 πνt dν −∞

∞ ∞

ψ c (t , f ) =

∞

∫ ∫ Ψ (τ, ν)e

j 2 π ( ντ − fτ )

c

− ∞− ∞

∞

.

Eq. 3.30

dτdν = ∫ Φ c ( f , ν)e j 2 πνt dν −∞

The AF domain kernel Ψc(τ,ν) can be interpreted as the frequency response of a 2-D filter. This kernel should be as close as possible to an ideal low-pass filter in order to allow good cross-term reduction, whith little auto-term distortion. The Cohen class is defined for continuous signals. O’Neill and Williams [147] [148] extended this class to encompass the TFDs of discrete signals, with the introduction of four subclasses. The HRECG signal can be included in the type II class, i.e. discrete and aperiodic, and hence it should be analysed by the type II Cohen class TFDs. It should be mentioned that this has not been the normal practice in the published literature on VLP analysis. There are numerous TFRs grouped in the Cohen class. Besides the spectrogram, the WD and its modifications (PWD and SWD), several more are reviewed elsewhere [52] [5] [38] [147]. Most of them are named after their developers: Choi-Williams, Born-Jordan, Richaczek, Page, Levin, Claasen-Mecklenbräuker, Margineau-Hill, etc. Only a few of them, however, have been used for VLP analysis. Figure 3.2b compares the t-f plots of the same SAECG (see Figure 3.2a) after applying some of the type II Cohen class TFDs developed in [147]. It can be appreciated that the spectrogram is the only non-negative bilinear TFR. The WD (quasi-WD in this case) has a very good resolution in the t-f plane, but it includes cumbersome cross-terms. The

78


spectrogram smoothes the excessive cross-terms at expense of auto-term attenuation and resolution reduction in general.

Filtered QRS complex 55

50

45

40

Amplitude (uV)

35

30

25

20

15

10

5

0

0

50

100

150

200

250

Time (ms)

Figure 3.2a Time domain analysis of the SAECG (X-lead, p15b).

79


Figure 3.2b Analysis of a high-pass filtered SAECG (X-lead, p15b) by different TFDs.

The HRECG analysis in the t-f plane is TFD-dependent. The number of cross-terms and auto-terms, and the resolution depend on the fixed window or kernel associated with the

80


particular TFD. These TFDs perform well only for limited classes of signals. It can be concluded that the relative performance of the various TFDs depends on the signal. The Affine class of TFDs

The TFRs that satisfy Eqs. 3.2 and 3.3, i.e. time-shift and scale covariant, are grouped in the Affine class. The scalogram is included in this class, along with the Bertrand’s Po and the Unterberger distributions [76]. Several TFDs belong to both, the Cohen and the Affine classes.

This is the case of the WD, Ackroyd, Born-Jordan, Choi-Williams,

Margineau-Hill, exponential and Richaczek distributions [38]. The Affine class TFDs are useful when detecting short duration transients, such as the VLPs and the abnormal intra-QRS waveforms in the HRECG. Many TFDs in this group permit multi-resolution analysis. The Affine class can be expressed by similar equations as the Cohen class (Eqs. 3.283.30). Here, the features of the TFD also depend on the fixed kernels ϕa, Φa, ψa, and Ψa, associated with the particular TFD. In the case of the scalogram, for instance, the analysis depends on the particular wavelet family selected. The best results are obtained when the wavelet resembles the features of the signal of interest. However, it is not possible to find a unique wavelet family that can track the characteristics of highly variable waveforms, such as the VLPs. 3.4.4 Signal-dependent kernel TFDs

Baraniuk and Jones [37] developed the theory of the signal-dependent kernels, which overcome limitations of the fixed-kernel methods. It should be mentioned that the signal-

81


dependent kernel TFDs are no longer bilinear [52]. To obtain the signal-dependent kernel, the AF is calculated. The function of the kernel, f[Ψ], is ∞ ∞

f [Ψ ] =

∫ ∫ AF (τ, ν)Ψ(τ, ν)

2

x

dτdν .

Eq. 3.31

− ∞− ∞

Since the auto-terms are concentrated around the origin, the kernel should never increase in any radial direction.

To control the kernel concentration around the origin, the

parameter αc is used, ∞ ∞

∫ ∫ Ψ(τ, ν)

2

dτdν ≤ α c .

Eq. 3.32

− ∞−∞

The larger αc, the more concentrated the kernel will be [37].

Figure 3.3 Analysis of a SAECG (X-lead, p15b) by the adaptive optimal-kernel TFR.

Adaptation of the kernel over time to track signal variations, through a short time AF [101], provides good performance. Figure 3.3 shows the analysis of the same signal used in the previous figure by using an adaptive optimal-kernel TFR [101].

82


3.5 Information extraction from t-f images of the HRECG Several studies of VLPs in the t-f plane have been based just on a visual (subjective) characterisation of the signal [140] [78]. However, for a clinical application of these analysis methods, some objective measures have to be implemented in order to extract the information contained in the t-f images.

The specific techniques to extract this

information depend on the properties of the TFR used [75]. In this section, several examples of the feature extraction from the t-f image are introduced in the context of the HRECG studies. A method was developed by Waldo et al. [212] in which all the information for each pseudo WVD was condensed into a pair of numbers in the t-f plane, resembling the average frequency and average time computed from the pseudo WVD, i.e. the instantaneous frequency and the group delay. These “centres of mass” were plotted without averaging and it was found that they formed fairly dense clusters from the same patient group, with acceptable separation between different clusters. These results showed that computing the centres of mass over the entire frequency range (0-250Hz) produced good clustering and separation between the MI and the VT clusters. The X-lead was found to give the best results while the Z-lead gave the poorest. Contrasting with the previous results [212], it has been reported that, although the instantaneous frequency and the group delay can give useful insights of mono-component signals, they are unsuitable for multi-component and noisy signals [2] [5] [38]. It should be noticed that, unfortunately, this is precisely the case of the HRECG signal.

83


Waldo also used an alternative time and frequency area function determined from whether the signal energy was either present or absent (relative to a threshold) at a given timefrequency location [212]. There does exist a particular region in the t-f plane whose energy may help to discriminate between VLP and non-VLP subjects. According with the characteristics of the VLP, this region is expected to be located on the higher frequencies comprising the late QRS segment. Dickhaus and Heinrich [61] discussed which region allowed a better separation of VLP and non-VLP groups. The computation of energy in a particular region of the t-f plane has been the method most frequently used to extract the VLP information from the t-f image. Some authors [164] [162] have quantified an energy percentage to obtain information even from the crossterms of the WD. They measured the energy from 60 to 250Hz for the frequency domain and from QRS onset to QRS offset for the time domain, and the energy from 0 to 250Hz limited by the same time boundaries to compute the energy percentage. This index was found to be higher for healthy subjects because the intra-QRS components for them are neither attenuated nor delayed. However, more experimentation is required to confirm these results [162]. A group at the LMU [179] defined a factor of normality, NF, to classify the maximum entropy method results. This NF was calculated as a ratio of energy regions between an area far outside the QRS complex and the area at the end of the QRS. The idea of the NF has been re-visited by other researchers [30]. Non-VLP subjects exhibit energy distributions that rapidly decay to zero, while VLP patients exhibit extended fractionation (in one or two leads) characterised by a slow rate of

84


decay of the energy in the t-f plane [128]. The settling time was computed to quantify the extent of the fractionation in the t-f plane and its values for VLP patients was found as twice as long as those for non-VLP patients. Several optimal strategies of decision can be reformulated in the t-f plane [5]. Different detectors have been implemented in the t-f plane [184] to evaluate the VLPs and the abnormal intra-QRS waveforms. Lander and Berbari [122] [123] introduced the t-f plane Wiener filtering [93] to the study of the VLPs. The Wiener filtering in the wavelet domain [111] is another emerging technique that has been applied to the detection of VLPs [160].

3.6 Wavelet transform as a special linear TFR When the frequency content of the signal varies too fast, like in the case of the notches and slurs in the HRECG, the frequency content becomes smeared over the whole spectrum. By using narrowband basis functions (sinusoids in the STFT), the wideband signals, such as the VLPs, cannot be accurately represented. The wavelet transform (WT) allows for a better representation of such signals. The continuous wavelet transform (CWT) for a continuous signal x(t) is defined as

CWTx ( τ, a ) =

∞

⎛t −τ⎞ x ( t )ψ * ⎜ ⎟dt , ⎝ a ⎠ a −∞

1

∫

Eq. 3.33

where ψ(t) is the mother or basic wavelet, which is typically a band-pass function centred around fo, and a is the scale factor, which can be thought as B/fo [204]. A larger value of a generates a compressed ψ(t/a) that allows a better time localization. The compression and

85


expansions of ψ(t) allow for variation of time and frequency resolution, in contrast with the uniform resolution of the STFT. Another interpretation of the WT conducts to a bank of filters,

⎛t⎞ ψ⎜ ⎟ , whose bandwidth is changing with frequency. a ⎝a⎠

1

The CWT is

covariant by translation in time and scale because it satisfies Eqs. 3.2 and 3.3. The CWT redundancy makes all information more visible, which may be helpful in the analysis of subtle details like those of the VLPs in the HRECG. This explains the common use of the CWT4 in VLP analysis [140] [78] [177] [128] [61] [175]. However, the CWT gains in readability at expense of space and increasing computation load. In Eq. 3.33, the dilation/contraction parameter a and the translation parameter τ can be discretized as a = ao j ,

ao > 1,

τ = kao j τo ,

j∈Ζ

τo ≠ 0,

k ∈Ζ

.

Eq. 3.34

For computational efficiency τo=1, and ao=2, which yields a binary dilation 2j and a dyadic translation 2jn (dyadic scheme). The function ψ(⋅) may be built with a set of j 2 ψ j , k = 2 ψ j (t − 2 − j k ) , −

orthonormal wavelets

which ensures a unique and complete

representation of a signal. This may be express as: ∞

ψ j, k , ψ j ', k ' =

j = j' ⎧1, if ψ ψ = ( t ) * ( t ) dt ⎨ j , k j ' , k ' ∫ ⎩0, otherwise

−∞

4

Not really continuous wavelet because the signal is discrete.

86

and

k = k'

. Eq. 3.35


Each of the orthogonal vector spaces in orthogonal wavelet basis offers different levels of resolution and scale, i.e. multi-resolution signal decomposition. Smaller scales help to explore fine details (higher resolution), while larger scales conduct to global view of a sub-sampled signal. A signal x(t) can be exactly represented (synthesised) as a weighted sum of basis functions, x (t ) =

∑ ∑ C j , k ψ j , k (t ) ,

Eq. 3.36

j∈Ζ k ∈Ζ

where Cj,k are the associated coefficients of the WT. In contrast with the STFT (BalianLow theorem), there do exist functions ψ(t) that can be used as prototype wavelets to obtain orthonormal bases and for which the product TB is a finite number. The wavelet orthogonal scheme has been extended to synthesis functions ψ’j,k(t) ≠ ψj,k (t) leading to biorthonormal wavelet bases [59]. 3.6.1 Orthogonal wavelets and multi-resolution scheme

Mallat proposed a fast pyramid algorithm (Figure 3.4) to compute the WT based on consecutive filtering to decompose the signal in approximations (high-scale, lowfrequency components of the signal) and details (low-scale, high-frequency components), introducing down-sampling to keep the amount of data approximately constant [29] [170] [218]. Unfortunately, the involved sub-sampling makes the conventional orthogonal WT translation variant, i.e. the output is dependent of the position of the input signal [159]. Several methods have been used to overcome this translation variant in different

87


applications [50] [151] [55] [56].

Alternative discrete translation invariant wavelet

algorithms are available in commercial software, including the Wavelab [60] and the Wavelet Toolbox for use with MATLAB, R12 [138].

LPFd

cA3

cA2 LPFd

cA1

cD3 HPFd

LPFd

x

cD2

x

HPFd

cD1 HPFd

LPFd

Low-pass filter for decomposition

HPFd

High-pass filter for decomposition

x original signal cAj approximation coefficients of the j-th level

Down-sampling or dyadic decimation

cDj detail coefficients of the j-th level

Figure 3.4 Multiple level decomposition (analysis) by the pyramid algorithm.

Several VLP studies have been based on the multi-resolution analysis of the HRECG [30] [204]. Figure 3.5 shows an example of this kind of analysis performed on a SAECG of 256 samples (256ms), by using 6 levels of decomposition. It should be noticed that the lower scales show the finer details (d1, d2), while the higher scales (d5, d6) have associated the coarser details. In this example, up to 8 levels of decomposition could have been performed (28=256) but no relevant information is contained in those higher levels as can be deduced from d6. There are various algorithms available to estimate the optimum level of decomposition [58].

88


Figure 3.5 Six-level decomposition of the SAECG (Y-lead, fp26) showing the original signal (s), approximations (a), details (d) and coefficients (cfs).

The inverse discrete wavelet transform (synthesis) can be estimated by using a complementary process of the multiple-level decomposition. Figure 3.6 illustrates the reconstruction of the signal x, given the coefficients (approximations and details). The upsampling block inserts zeros between successive samples.

89


LPFr

cA3

cA2 LPFr

cA1

cD3 HPFr

LPFr

x

cD2

x

HPFr

cD1 HPFr

LPFr

Low-pass filter for reconstruction

HPFr

High-pass filter for reconstruction

x reconstructed signal cAj approximation coefficients of the j-th level cDj detail coefficients of the j-th level

Up-sampling

Figure 3.6 Reconstruction algorithm (synthesis).

∞

The basic wavelet ψ (

∫ ψ( x )dx = 0 )

is usually associated with a scaling function φ

−∞ ∞

(

∫ φ(x ) = 1 ) that allows fast WT implementation.

Between 2 successive scales, there are

−∞

twin-scale relations given by, φ j +1,0 = ψ j +1,0 =

∑ hk φ j,k

k ∈Ζ

∑ g k φ j,k

,

Eq. 3.37

k ∈Ζ

where h is a finite impulse response (FIR) low-pass filter (or scaling filter) and g is a FIR high-pass filter (or wavelet filter) for reconstruction (synthesis), marked in Figure 3.6 as LPFr and HPFr respectively. The filters h and g constitute conjugate quadrature filters or quadrature mirror filters (QMF), i.e. the coefficients of g can be obtained by flipping those of the h, and inverting every other coefficient. That is, g (k ) = −1k h(2 ⋅ O − 1 − k ) ,

90

Eq. 3.38


where O is the order of the basic wavelet. The FIR low-pass filter for decomposition (LPFd in Figure 3.4) can be obtained by flipping the coefficients of the LPFr, as well as HPFd is formed by the flipped coefficients of HPFr. HPFd and LPFd constitute QMFs. 3.6.2 Wavelet Packets as a generalization of the wavelet decomposition

The Wavelet Packets (WP) algorithm can be seen as a generalization of the wavelet decomposition scheme. Here, not only the approximation can be split (as the case of the wavelet decomposition), but also the details, as shown in Figure 3.7. Therefore, for an Llevel decomposition, there are 2L different ways to decompose the signal, in contrast with the wavelet scheme, which has only L+1 possible ways. It should be noted, however, that the wavelet decomposition is a subset of the WP method.

AAA(3) AA(2) DAA(3) A(1) ADA(3) DA(2) DDA(3) x=A(0) AAD(3) AD(2) DAD(3) D(1) ADD(3) DD(2) DDD(3)

Figure 3.7 Three-level WP decomposition tree.

To select the optimal decomposition, different approaches have been taken, but the most popular ones are entropy-based [58]. That entropy must be an additive cost function such

91


that the decision of what route should be followed (or if no other level is needed) can be determined by easy comparison at every node. Among these additive cost criteria, can be mentioned those based on the Shannon entropy, the norm, and the logarithm of the energy of the signal [5]. The WP representation gives information on time localization, scale and frequency. Due to the characteristics of the WP atoms, the naturally ordered coefficients obtained by this algorithm do not follow a monotonically increasing of the main frequency and they need to be re-arranged (frequency ordered) to analyse a signal. Unlike the WT, the WP provides good frequency resolution at arbitrary analysis frequency. 3.6.3 Bi-dimensional WP analysis

Sometimes the signal of interest is represented as an image (2-D representation) and some techniques for image processing are required [157]. The WP (and the WT) can be used for image decomposition and analysis. 2-D WP analysis is an extension of the 1-D case as the QMF algorithm extends to multi-dimensional signals by separation of variables. For these kinds of signal (image), one-level decomposition yields four sub-band images, as shown in Figure 3.8. The four sub-band images are produced by the combinations of low-pass and high-pass filters (LPF and HPF, respectively) applied to the each row and column. If the LPF is applied to the rows and the HPF is applied to the columns, then the horizontal elements are preserved (blue colour in the figure). In the same way, the vertical elements are preserved after applying the HPF to the rows and the LPF to the columns (green).

The combinations HPF-HPF (red) and LPF-LPF (black) keep the diagonal

92


elements and the overall trend features, respectively.

The initial image can be re-

constructed by using an adequate sub-set of the sub-band images.

Figure 3.8 Bi-dimensional WP decomposition (2 levels). 3.6.4 Wavelet denoising

WT and WP techniques are very attractive for the development of compression and denoising algorithms. In this sub-section, attention is focussed on denoising as it is more applicable to the VLP analysis problem. Due to the vanishing moment property and the compact support of wavelets, after applying the WT (or WP), most signal energy is clustered in a few non-zero coefficients, whereas noise energy is spread over all coefficients. Therefore, the signal can be represented by a few wavelet coefficients.

93


Reconstructing the signal using only these few coefficients can effectively reduce the noise in the signal. Denoising based on WT and WP can be applied to both 1-D signals and 2-D signals as well. For the sake of simplification, all the explanations here are given for the 1-D case, but the same technique can be expanded to the 2-D case (image denoising). There are different techniques to perform the denoising in the wavelet domain. One of them is based on the direct multiplication of the wavelet coefficients at adjacent scales [217]. This method enhances the important signal edges, while suppressing noise. A research group at the University of Patras, Greece, used this algorithm [43] [149] [152] and reported that the variance of noise can be forced to a very low value, however the VLP components may be drastically attenuated at the same time.

x[k]= s[k]+ n[k] 1γ

.

Eq. 3.41

The soft thresholding has been, however, the most frequently used thresholding, in general and in specific HRECG applications [7] [160].

96


3.6.5 Wavelet families

For the implementation of the WT (and the WP transform) a wavelet family is needed. This family consists of the mother wavelet ψ and the scaling function φ if it exists. There are numerous wavelet families [59] available, whose suitability for a specific application is determined by: •

The speed of convergence of ψ and φ (if it exists) to zero when the time tends to infinity. This is the compact time support, which determines the time localization [191].

•

The speed of convergence of the FT of ψ and φ to zero when the frequency tends to infinity. This is the compact frequency support, which determines the frequency localization.

•

The regularity (differentiability), which is associated with the smoothness of the reconstructed signal.

•

The symmetry, which avoids dephasing in image processing.

•

The (bi-)orthogonality of the resulting analysis, which generates a space-saving code.

•

The number of vanishing moments, which is important for compression algorithms.

•

The existence of explicit expression.

97


Morlet

Gaussian

Meyer

(n-th

Daubechies

Symlets

Coiflets

Bi-

(order O)

(order O)

(order O)

orthog.

derivative)

Complex

pairs

Regularity

Infinitely differenti able



0.2⋅O, for large O

Arbitrary

Arbitrary

Support width

∞, effective [-4 4]



2⋅O-1

2⋅O-1

6⋅O-1

Symmetry

Yes

Symm. if n even.

Yes

Far from

Near from

Near from

Yes

Yes

-

Of ψ, O

Of ψ, O

Of ψ, 2⋅O

Yes

-

Antisymm. if n odd Vanishing moments

-

-

Of φ, 2⋅O-1 Orthogonal

No

No

Yes

Yes

Yes

Yes

No

No

Biorthogonal

No

No

Yes

Yes

Yes

Yes

Yes

No

Continuous transform

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Complex

Discrete transform

No

No

With nonFIR

Yes

Yes

Yes

Yes

No

Fast algorithm

No

No

No

Yes

Yes

Yes

Yes

No

Explicit expression

Yes

Yes

No

No

No

No

For splines

Yes

Comment

No φ, no exact reconst.


O = 1 is Haar wavelet


n = 2 is Mexican hat

Table 3.1 Characteristics of the most popular wavelet families.

Table 3.1 reviews the characteristics of the most popular wavelets [138]. Among them can be distinguished the crude wavelets, which comprise the Morlet and the Gaussian 98


wavelets (the n-th derivative of the Gaussian probability density function). These crude wavelets are infinitely differentiable and have explicit expressions. Daubechies (including the Haar wavelet), symlets and coiflets of different order O are appealing for their compact support. Meyer wavelet (and its discrete version) is a compromise between these wavelets and the crude wavelets. The spline bi-orthogonal wavelets try to integrate the good features for analysis and synthesis into a pair of independent wavelets (one for analysis and one for synthesis). There are also available complex wavelets, such as the complex Morlet, the complex Gaussian, the complex Shannon, and the complex frequency B-spline wavelets. Morlet et al. first applied wavelet analysis to the high-resolution signal-averaged ECG in 1993 [139]. Since then, numerous studies of VLPs have been based on the Morlet wavelet [140] [78] [128] [61]. This wavelet has an explicit expression and is easy to compute. The analysis with this basic wavelet allows for a quasi-continuous representation, as illustrated in the example of Figure 3.10. The Morlet wavelet is a modulated Gaussian window that leads to the best compromise for a good t-f concentration because of the Heisenberg-Gabor principle. However, all conventional wavelet analysis implies a tradeoff between time and frequency resolution. To overcome the t-f trade-off, looking for a denser representation, Meste et al. [140] combined two analyses with a modified Morlet wavelet, one for high temporal resolution and the other for high spectral resolution. The same idea, with a vector sum, was explored by Lichorwic et al. [128]. Gramatikov [78] used 12 different scales, grouped in 3 sets, to obtain a smoother and more continuous representation of the spectral components. Other

99


reported analyses of VLPs have used the Lemarie’s wavelet [18], the harmonic and musical wavelets [30], and the symlets [160].

Figure 3.10 Analysis of SAECG with the Morlet wavelet (Y-lead, fp26).

3.7 Summary Spectro-temporal graphics reveal that VLPs, like some other abnormal intra-QRS potentials [44] [42], have a time variable energy spectrum [121], which constrains the use of the classical Fourier analysis technique. To analyse the rapid spectral changes in VLPs, a TFR may be useful. T-f analysis of the VLPs potentially provides more information [107] and solves some of the limitations of the independent time and frequency domain analyses. Different t-f transforms have been used for VLP analysis. Some of these transformations use a parametric model, like the AR model in adaptive frequency determination, while others involve Fourier decomposition or WT. 100


The AR modelling procedure assumes a harmonic structure for the HRECG [140]; however, no significant harmonic components are present in the HRECG [123]. Furthermore, AR modelling methods are unstable, susceptible to noise interference, and require optimal recording units (very low noise, little distortion of signals, 16-bit A/D converter) [124]. T-f transforms using Fourier or wavelet decomposition have some advantages for detecting VLPs, since such signals have characteristic position (temporal localization), nowell known spectral range, and a spectrum that is mixed with the broadband spectrum from the QRS complex [140]. The STFT, WT and WD are examples of this group of TFRs. One of the most commonly used TFRs for slowly time-varying or quasi-stationary signal is the spectrogram [78], which is equal to the square magnitude of the STFT. The quadratic spectrogram smoothes away all cross terms, except those that occur when two signal components overlap, as in VLP analysis. This smoothing also distorts auto-terms. Thus, the spectrogram produces too much smearing in both time and frequency directions for VLP studies [124]. The WD achieves the maximum time and frequency simultaneous resolution in VLP detection [124] [61]. However, large interference terms are present. Interference must be smoothed using a kernel or smoothing function [52] designed to attenuate the interference, but such a function will also lower the resolution of auto-components, or signal terms [140] [122]. Some modified WDs have been used to detect VLPs [140] [78] [122], but the results are limited.

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The WT uses a special sliding analysis window, the mother wavelet, which is either compressed or dilated to give a multi-resolution signal representation [139] [140] [78] [61]. The scalogram, which is the squared magnitude of the WT, can be thought of as a multi-resolution output of a parallel bank of octave band filters. One drawback of the scalogram is its poor temporal resolution at low frequency regions of the t-f plane and poor spectral resolution at high frequencies. Moreover, the scalogram cannot remove cross-terms when signal components overlap [124] [61] [53]. Some literature comparing the behaviour of the classic TFRs claim the WT as the best choice for HRECG signal analysis [124] [61]. Several modifications have been proposed to increase the wavelet resolution in VLP studies [131] [78] [116], but it needs to be increased even further. The main problem of the t-f analysis proposed for VLP studies is its lack of simultaneous resolution in time and frequency axes [126]. The low t-f energy concentration makes distinction between normal and abnormal signal components difficult [122]. In addition, the reproducibility of these tests is very poor [209]. Therefore, they are not reliable for clinical applications in their present state.

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Chapter 4 - HRECG database design

Chapter 4 - HRECG database design 4.1 Introduction To evaluate the new algorithms developed in this thesis, and compare their performance to previously published techniques, a bank of test signals is required. While simulated cardiac signals can be used for initial assessment of algorithm performance, the complex nature of the ECG demands a more accurate signal model. For conventional ECG processing algorithms, the most often used test signals are those of the MIT-BIH database, held at MIT. This source has been used by many researchers to evaluate such signal processing schemes as arrhythmia detectors and data compression techniques over a wide range of pathological conditions. Several other databases of conventional ECG records are also available, but unfortunately, this is not the case for the HRECG. Numerous papers on the topic of VLP detection refer the use of databases collected by the individual authors for particular purposes [210] [23] [187] [81] [216] [61]. In most cases, the number of subjects is very small [83] [51] [140] [192] [128] [43], or limited to a very specific ailment, e.g. Chagas disease [81]. In the majority of cases, the signal stored is only the filtered QRS complex or the averaged waveforms with no information of the original signal and noise; therefore, its usefulness as a test signal for all the algorithms involved is limited. The desired test signal, suitable to validate all the algorithms involved in a HRECG analysis system, should consist of a relatively long sequence (~300 beats) of every individual lead (X, Y and Z). Consequently, it was decided to construct a HRECG database as part of this thesis. To provide an accurate signal model, it was decided to

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derive the database from actual clinical HRECG recordings, which in turn necessitated the collection of clinical data. Although there are several commercial HRECG systems available, all are prohibitively expensive and most of them do not meet the accepted standards [26]. In addition, these commercial systems are not flexible enough to permit the incorporation of new signal processing developments [88]. As a suitable alternative, a personal computer (PC) based system was designed and developed in this thesis. This PC-based system consists of an analog front-end to condition the ECG signal, a 16bit A/D card as an interface with the PC, software to control the acquisition and data storing in the PC hard drive, and software to perform the offline analysis. The front-end was built at the Institute of Biomedical Engineering, University of New Brunswick, as a general-purpose system and adapted to this application [207]. IOTech [97] provided the A/D card and a sample and hold (S/H) board preceding it. The acquisition software was programmed in LabView [190] and the analysis software used the Graphics User Interfaces (GUIs) of MATLAB 5.3 (tested to be fully compatible with MATLAB 6.0, R12).

4.2 Front-end and acquisition process For the HRECG acquisition, 7 single-use Ag/AgCl electrodes (Red DotTM) were placed over the skin surface according to the standard XYZ lead system (Figure 2.3). Along with the leads X, Y and Z, a common mode signal Vcm was also collected.

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Figure 4.1 Analog front-end. 4.2.1 Front-end hardware The analog front-end system (Figure 4.1) consists of 4 identical channels [207]. Each channel includes a low-noise FET-input differential amplifier, an optically isolated amplifier (Burr Brown ISO100) and low-pass and high-pass filters (LPF and HPF, respectively) to reject interference and reduce the noise level by limiting the bandwidth.

Figure 4.2 Data conversion and storing.

105


Several gain values can be selected (100, 200, 400, 600, 800 and 1000), as well as highpass cutoff frequencies of 10Hz, 0.5Hz and DC coupling. Two stages of active Bessel LPFs are used as anti-aliasing filters. The first one is a 4th order with a fixed cutoff frequency of 30kHz and the second one is an 8-pole programmable filter (Frequency Devices 828L8L4) that can be adjusted from 100Hz to 25.6kHz, with a step of 100Hz. The acquisition system also includes a simultaneous sample and hold (S/H) card, DBK17, and an A/D board, DaqBoard 216/A, both provided by IOTech [97]. This part of the system, shown in Figure 4.2, is responsible of data conversion and storing. The S/H card eliminates time skew between the 4 channels. The DaqBoard 216/A has a 16-bit A/D converter with a ±5V bipolar input range.

Figure 4.3 Main window of DaqView 7.0.

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4.2.2 Front-end software To control the acquisition process from the PC, the DaqView 7.0 [97] software was initially used. Figure 4.3 shows the main window of this program. This general-purpose acquisition software was offered by the A/D board provider, but was deemed “too complex” to be operated by the medical and paramedical personnel. Consequently, to simplify commands and to make the process more user-friendly, the software Daq_216A was developed [190] using the LabView drivers provided by IOTech [97]. Figure 4.4 shows the simplicity of this user interface as compared to Figure 4.3.

Figure 4.4 Window of Daq_216A software.

107


4.2.3 Front-end settings For this application as a HRECG system, the differential gain was fixed at 800 on the front panel of the analog hardware, to avoid saturation during the peaks of the signal. However, the total gain of the system can be changed from the control software to be ×2, ×4, or ×8 of the fixed gain. This gain coupled with the 16-bit A/D converter gives a

signal resolution better than

5V = 0.19µV 800 ⋅ 215 − 1 .

(

)

Most of the data acquisition for this

work was performed at a total gain of 3 200. In a few cases, a different gain was used, but the resolution was always much better than the 2.5µV recommended in the standards [26]. The sampling frequency used was 1kHz, although this can be changed from the acquisition control software. The cutoff frequency chosen on the front-end for the HPF was 0.5Hz and the LPF, used as an antialiasing filter, was set to attenuate the frequency components over 300Hz. According to the frequency response of an 8-pole Bessel LPF, at the Nyquist frequency

fs (500Hz), the attenuation provided is approximately -9dB, 2

that is, around 8 times. This attenuation at the Nyquist frequency can be increased to around –40dB (1:10 000) if a sampling frequency of 2kHz, rather than 1kHz, is selected, but the amount of data to be stored will double and the speed at which the data can be processed will decrease. However, this higher sampling frequency may be a better choice if a more powerful computer is available.

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4.2.4 HRECG data files Data from the standard 4 channels (X, Y, Z, and Vcm) were collected from approximately 120 subjects in total. Each record lasted 5 minutes, which permitted the collection of over 300 heartbeats.

Because of the sampling frequency of 1kHz and acquisition

duration of 5min, every file contains 300 000 samples of each channel, that is, 1 200 000 samples (of 16 bits each) in total. This file is stored temporarily on the hard disk of the PC using a special binary format that requires 2 344kbytes for every subject. This binary file takes the name specified by the user from the control software and uses an extension IOT. After generating the IOT file, the control software creates a descriptor file with the same name of the binary file and extension IO$ to refer the characteristics of the acquired file. This descriptor file carries information about the sampling frequency and the resolution (1/LSB) of every channel, as shown in the example of Figure 4.5. *TYPE DAQVIEW 5.0 *FORMAT BINARY *FREQUENCY 1000.000000,1000.000000 *PRETRIG_COUNT 000000000 *CHANNELS 00000,20.970881,X,microV, 00001,20.970881,Y,microV, 00002,10.485440,Z,microV, 00003,20.970881,Vcm,microV, Figure 4.5 Example of descriptor file (.IO$).

109


4.3 General information of the DSP software The digital signal processing (DSP) software was programmed using the GUIs of MATLAB 5.3 and later updated to MATLAB 6.0, Release 12. MATLAB is a popular and powerful quantitative programming environment [28] that allows very fast prototyping of algorithms, using high-level commands. In addition, a large number of algorithms suitable for DSP are available as part of the MATLAB function libraries and toolboxes [5] [129] [138]. Since MATLAB code can run on different platforms, from simple PCs to state-of-the-art scientific workstations, reproducibility is guaranteed. In addition, the MATLAB 5.3 (MATLAB 6.0) GUI tools allow a fast and easy implementation, adding flexibility to the design. The DSP software includes several algorithms to manipulate and display data and results in a user-friendly environment. First, the selected data file is loaded from the PC hard disk to display the HRECG leads. Then, the user can reduce the powerline interference, and detect the fiducial marks (Chapter 5). After this pre-processing, the standard analysis of the VLPs (Simson test) can be performed, as well as alternative novel techniques (Chapter 6).

All pre-processing stages mentioned above are part of a general risk

stratification system, which will eventually include Heart Rate Variability tests (not part of this thesis) along with the VLP analysis. The off-line analysis of the HRECG signal, collected by the acquisition block and stored in the PC hard drive, starts loading the digital file into the Stratification.m MATLAB GUI environment. After the user selects a file with extension .IOT from the PC hard drive, the information on the sampling frequency and resolution of every channel is extracted from the associated descriptor file (Figure 4.5). Then, the screen shows a

110


segment of the individual leads in a format similar to conventional electrocardiographs or bedside monitors (Figure 4.6).

Figure 4.6 Risk stratification software main window. The user can select one, two, or the three XYZ leads at a time. The amplitude of the signals on the screen can be adjusted, changing the “gain”. The default value is ×1, which corresponds to an interval of ±2mV on screen. In addition, a “zoom in” (in the yaxis) can be done with the option ×2, which allows seeing an interval of ±1mV, as well as a “zoom out” when ×½ is selected (±4mV). On the time axis, 3 options are also available, referring to the equivalent standard speeds in standard electrocardiographs. The default speed is 25mm/s, which corresponds to a 4-

111


second segment on screen. The two “zoom” levels available (in the x-axis) are 50mm/s (2-second segment) and 100mm/s (1-second segment). An optional grid is available. The user can also select the initial sample of a particular segment to be shown on the screen, or scroll the data to the right and to the left, looking for specific details, such as the presence of PVCs, powerline interference, EMG noise, etc. These features allow a general visual evaluation of the signal collected.

4.4 HRECG database To complete a representative HRECG database, two groups of subjects were recruited. The first group consisted of 59 post-MI patients during the first 2 weeks of evolution of the infarction; the other group included 63 healthy volunteers with no evidence of CVD. Data were collected in 3 different Hospitals in Santa Clara, Cuba, between June 1999 and April 2000. The hospitals and areas involved were the Intensive Care Unit (ICU) of the University Hospital “Arnaldo Milián Castro”, the ICU of the City Hospital “Dr. Celestino Hernández” and the Cardio Centre of Villa Clara. All the subjects had to sign written consent (Appendix A) previously approved by the Ethics Committee of those centres. General information from each subject was gathered and incorporated into the database. This included basic demographic information, such as race, gender and age; along with body mass index BMI5 and date of the data collection. The name and identification (identity card, or Clinic History) for future follow-up was kept confidential to assure anonymity of all subjects.

5

BMI is used to define nutritional status and can be calculated as

weight( kg)

(height( m) )2

. The range from 20 to 25

is the most acceptable. Over 40 can be considered as gross obesity, while below 16 as severe starvation.

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In the case of the post-MI patients, the location of the infarct, the use of thrombolytic agents and the days of evolution were also included in the database. This information was obtained from the patients’ medical records and from interviews of the patients, their relatives and physicians. Comments on the presence of CVD risk factors (high blood pressure, diabetes mellitus, etc.), PVCs, and the quality of the data collected, were also included. Recordings were performed in an unshielded room, which in the case of the patients was the ICU room. Good skin preparation was used prior to placing of the electrodes to assure low levels of noise and interference. This involved cleaning of the skin surface with alcohol, shaving if necessary and lightly abrading the skin with the sandpaper available on the Red DotTM electrodes. The Ag/AgCl electrodes were placed according to the standard XYZ system (Figure 2.3). Subjects remained in a supine position and as relaxed as possible during the data acquisition period. Data collection was done in warm surroundings and far away from interference sources such as fluorescent lights, air conditioning and motors, whenever possible. 4.4.1 Statistics The non-confidential information collected along with the ECG data appears in Appendices B and C. The post-MI data (Appendix B) consists of 74 XYZ records collected from 59 different patients. In addition, 74 XYZ records were collected from a group of 63 healthy volunteers with no evidence of CVD (Appendix C). The demographic composition of the patients group is as follows: 55 subjects were white (93.2%), 3 were black (5.1%) and 1 was Asian (1.7%). There were 49 men (83%) and 10 women (17%) with ages between 32 and 89 (59±13 years old). Their weight varies from 113


45 to 105kg (70±13kg), and their height from 150 to 198cm (168±8cm); consequently, the body mass index (BMI) of the group varies from 19.2 to 34.4kg/m2 (25±4kg/m2). MIs can be classified according to the evolution timing as acute (6h to 7 days), healing (7 to 28 days) and healed (29 days or more) [4]. In this database, 55 records (74.3%) were collected when the patients were in the acute stage and 19 (25.7%) in the healing stage. More specifically, they were between the days 0 and 25 of evolution of the MI (4.4±4.6 days). Another way to classify MIs is by their location, on the wall of the left ventricle that was damaged during the event [166]. In this case, MIs can be referred as anterior, lateral, inferior, posterior or septal or a combination of locations. This database includes 36 records (48.6%) of patients who had damage in the anterior, 5 (6.8%) in the lateral, 25 (33.8%) in the inferior, 8 (10.8%) in the posterior, and 21 (28.4%) in the septal wall. Almost 53% of the patients (31) received anti-thrombolytic treatment, which should reduce the size of myocardial tissue affected. Bundle branch block (BBB) is associated to a wide QRS complex, which mask VLPs in the classical time domain analysis [26]; 12 subjects (20.3%), from which HRECG data were collected, suffered from some kind of conduction block. The rest of the information gathered from the medical records of the patients in the database showed that 24 (41%) suffered from hypertension (HBP), 7 (12%) from diabetes mellitus, 8 (14%) had angina, and 11 (18.6%) had had a previous MI (multiple MI) or were involved in a re-infarction process. 10 of the 59 patients (16.9%) presented PVCs during the 5-minute records collected.

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The group of the healthy volunteers (Appendix C) consisted 54 subjects of the white race (86%) and 9 of the black race (14%). 46 subjects were men (73%) and 17 were women (27%). The youngest person in the group was 18 and the oldest was 73 years old, with an averaged age of 42 (±13). The weights of these subjects were between 47 and 107kg (69±13kg) and their heights were between 157 and 190cm (170±7.8cm), averaging 23.9±3.9kg/m2 as BMI (16.7~31.2kg/m2). PVCs appeared in 3 of the 74 XYZ records (4.1%) of this group, while one subject (1.4%) had a BBB. 4.4.2 Noise characterisation Most SNR enhancement techniques assume that the background noise corrupting the signal of interest is white Gaussian noise. Unfortunately, this assumption is not always true and therefore the performance of the enhancement strategies is degraded. Consequently, attention was focussed on the statistics of the noise observed during the data collection. In order to characterise the noise corrupting the recordings, it was assumed that during the isoelectric segments no signal was present. This is a reasonable assumption as the heart is at rest during the isoelectric portion of the ECG. In addition, the noise is assumed to be quasi-stationary, that is, the noise statistics during the isoelectric segments are the same as during the signal components (QRS complex, or P and T waves). Therefore, a noise sequence resembling the HRECG background noise can be obtained by isolating sections of the isoelectric segments from the whole data record. isoelectric interval detector used here is explained in detail in Section 5.2.

115

The


Visual characterisation of the noise Figure 4.7 shows a typical example of the isoelectric segments extracted from an individual lead of the HRECG database. Although the powerline interference component can be easily observed in some records (as in Figure 4.7) and the global level of noise can be qualitatively estimated, this graphical time domain information does not reveal the nature of the noise. However, its power spectral density (PSD) can give a good visual description of the noise. The PSD is a frequency-domain description of a second order statistics of a stochastic process [87]. To perform this graphical characterisation of the noise, its PSD was estimated by using the Welch’s averaged periodogram method [100]. The data record was divided into 1024-sample overlapping (512-sample) segments. Every segment was multiplied by a Blackman-Harris window function and its periodogram was computed. An estimate of the overall PSD was then accomplished by averaging the individual periodograms. This reduces the error associated with a single periodogram estimate.

Amplitude (uV)

30 20 10 0 -10 -20 -30 0

100

200

300

400 time (ms)

500

600

700

Figure 4.7 HRECG embedded noise in the time domain (p50, X-lead).

116


Figure 4.8 shows the PSD of the noise associated to the previous figure. As opposed to white noise, which has a constant PSD for all frequencies, this noise shows a PSD decreasing with frequency.

In addition, the 60Hz component due to the powerline

interference can be easily seen, along with odd harmonics (180Hz, 300Hz and 420Hz). In this particular record, the ninth harmonic was so prominent that it appears as an alias at 460Hz (this emphasises the convenience of a higher sampling frequency in future data collection). Most raw records of this database show a certain degree of powerline (and its harmonics) interference, which is clearly distinguished from the PSD plots. In Section 5.3, the PSD of the remaining noise after interference cancellation is calculated and presented.

Figure 4.8 Estimated PSD of the noise (p50, X-lead). Analytical characterisation of the noise While the PSD gives a good visual characterisation of the noise, analytical parameters are needed to easily compare different situations and to know whether the noise can be assumed white Gaussian or not. In addition, it is important to know quantitatively the power of noise affecting the HRECG signal and the individual contributions of the powerline and its harmonics to the global figure.

117


The average power of noise n can be estimated from any of the plots mentioned above, that is, from the time domain signal, or the PSD (Eq. 4.1). The power Pn is the variance of the noise in the time domain, computed as the squared value of its standard deviation. From the PSD plot, the noise power can be estimated as the area under the curve. In general, the area under a specific portion of the spectrum can be interpreted as the fraction of the total signal variance due to the particular frequencies.

Hence, the

contribution of the powerline frequency and its harmonics can be estimated by integrating the associated portions of the PSD.

Pn =

σ n2

1 = 2π

0.5 f s

∫ Φ nn ( f )df

Eq. 4.1

− 0.5 f s

In the example record used for the explanation above (Figures 4.7-4.8), the noise power can be estimated and it is approximately 180.3µV2. From the PSD plot, the contribution of the powerline frequency and its harmonics to the global noise power can be determined.

In this case, it was estimated that the frequencies close to the 60Hz

component contribute to 68.4% (123.4µV2) of the noise power. The components around the third harmonic (180Hz) have a power of 7.0µV2 (3.9% of the total) and the components of the fifth harmonic (300Hz) have 0.7µV2, that is, 0.4% of the global amount.

The general contribution of the powerline frequency and its harmonics

(including the alias of the ninth harmonic) to the noise power is 132.7µV2, which is a 73.6% of the total. Previous studies have used the equivalent statistical bandwidth (ESB) and the whitening coefficient (WC) to analytically characterise biological noise. The ESB of a signal can be defined as the bandwidth of an ideal rectangular filter which, when fed from a white

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noise source, will yield an output variance-to-square mean ratio equal to that of the signal under test. This ESB [135] is given by 2

⎛∞ ⎞ ⎜ ∫ Φ nn ( f )df ⎟ ⎜ ⎟ −∞ ⎝ ⎠ . ESB = ∞ 2 ∫ Φ nn ( f )df

Eq. 4.2

−∞

If the PSD, Φnn( f ), is estimated as a discrete sequence of length M+1, that is, from 0 to M corresponding to the interval from 0 to

fs , the ESB can be estimated as 2 2

⎛M ˆ ⎞ fs ⎜∑Φ nn [i ] ⎟ ⎠ . ESB = ⎝ iM=0 ˆ [i ] 2 2M ∑ Φ nn i =0

(

)

Eq. 4.3

It should be noted that the higher the ESB, the closer the signal under test to be considered a white noise. In the case of a true white noise process, sampled at a frequency fs, the ESB will be the Nyquist frequency, that is, half the sampling frequency. The WC is a measure of the flatness of the spectrum [135]. It can be calculated from the estimated PSD sequence as the ratio of its geometric mean and its arithmetic mean, 1 /( M +1) ⎛⎛ M ⎞ ⎞ ⎜⎜ Φ ⎟ ˆ [ i ] ⎟ ∏ nn ⎟ ⎜ ⎜⎝ i =0 ⎟ ⎠ WC = 10 log10 ⎜ ⎟. M 1 ˆ ⎜ Φ nn [i ] ⎟ ⎜ M +1∑ ⎟ i =0 ⎝ ⎠

Eq. 4.4

A noise can be considered nearly white if its WC is between 0 and –2dB, while for a true white noise process, this parameter should be 0dB (its geometric mean is equal to its arithmetic mean).

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In the case of the signal shown in Figure 4.7, associated to the background noise in the Xlead of patient number 50 (p50), the ESB is only 4.9Hz, while the WC is –11.0dB. Therefore, it is clear as was assumed from the visual analysis: that this embedded noise cannot be considered as a white noise process. Unfortunately, most of the raw HRECG signals in this database fall into this category. Appendix D reviews the WC, ESB, the total noise power (Pt) and the partial contributions of the powerline frequency and its harmonics (P60, P120, …, Palias) for every record of the database (patients and healthy volunteers). This includes X, Y and Z leads, as well as the reference Vcm.

4.5 HRECG simulations Given the comparatively low frequency of occurrence of life-threatening arrhythmias, even among the post-MI patients (only 4 to 6% of them have an augmented risk within 2 years following MI [17]), the number of patients in the database expected to suffer from SCD is very limited. In addition, there is no reliable test, at present, to identify those at maximum risk. Unfortunately, the only infallible marker, sometimes, after a relatively long (2-year) follow-up period, is the manifestation of a lethal episode. Finally, the specific parameters to be obtained by performing a particular test with real HRECG signals are not certainly known. These facts conduct to simulations, as the only way to control characteristics of signals and noise and to know the results that should be expected from the beginning. A HRECG record y(t) can be modelled as the summation of a HRECG signal component x(t) and an additive noise n(t). The HRECG signal components can be obtained from a

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real data sequence after reduction of the background noise.

Several enhancement

techniques, which were mentioned in Section 2.3, can be used to reduce the variance of the noise in the isoelectric segments. To evaluate the algorithms developed, particularly in Chapter 6, a set of test signals was created. This set covers a wide range of HRECG waveforms, without and with VLPs, clean or extremely contaminated by typical ECG noise. The combination of synthesised and semi-synthesised waveforms provides a realistic and, at the same time, controllable environment for algorithm assessment. 4.5.1 HRECG basic waveforms To achieve a large variety of records, the basic waveforms (P-QRS-T segments) were extracted from real HRECG data, collected from 19 healthy volunteers and 15 post-MI patients, who did not present VLP in the standard tests. The non-VLP records to be used in these simulations were identified by using the standard VLP analysis in the time domain [26], which has a very high negative predictability, that is, the false negatives are uncommon (Section 1.2.3). The P-QRS-T segments of the three-lead (XYZ) system were pre-processed to ensure that the noise level was not higher than 0.3µV rms in any individual lead. Pre-processing included low-pass filtering and signal averaging to produce a P-QRS-T complex for each subject. In addition, several averaged records were manually edited, using Sound Forge 4.5 (Sonic Foundry Inc., www.sonicfoundry.com) to ensure that these single heartbeats were VLP free.

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For each subject, a 3-lead 5min record was constructed by concatenating approximately 300 identical P-QRS-T segments. These records constitute the clean non-VLP signals, which were the basis for the rest of the test set. Since all the P-QRS-T segments in each record were identical, the fiducial marks detected were perfectly periodic. 4.5.2 VLP records VLPs can be present or absent in a HRECG record. In order to simulate a VLP record, a synthesized waveform resembling the VLP characteristics had to be added to the nonVLP records. This allows predicting the outcome of the system in the presence of VLPs. VLPs are low-amplitude signals (~1-20µV), with short duration (~5-50ms) and broadband spectrum (~40-250Hz). These particular waveforms have been simulated as sinusoids, damped sinusoids, sinc functions and random processes. In this research, VLPs were simulated as coloured Gaussian processes, resembling better the real world signals. Three basic waveforms (Figure 4.9) were generated to resemble the characteristics of the VLPs in the XYZ leads. In this case, the basic VLP waveforms were obtained from 50ms random-generated sequences. The frequency content was limited by low-pass filtering (cutoff frequency of 250Hz) and then high-pass filtering (at 40Hz). The first sample of the sequences was forced to zero before filtering to avoid sharp transitions at the beginning. The filtered sequences were flipped in order to ensure a smooth transition at the end of the VLPs. The standard deviation of the 3 basic VLP waveforms was fixed at 12µV rms.

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20

X magnitude (dB)

X amplitude (uV)


10 0 -10 -20 150

200

10 0 -10 -20 100

150

200

Z magnitude (dB)

10 0 -10 -20 100 150 time (ms)

200

10 0 -10

250

0

100

200

300

400

500

0

100

200

300

400

500

0

100

400

500

20 0 -20

250

20

50

20

250

20

50

Z amplitude (uV)

100

Y magnitude (dB)

Y amplitude (uV)

50

30

20 0 -20

200 300 frequency (Hz)

Figure 4.9 Synthesised VLPs for the XYZ leads in the time and frequency domains. The basic VLP waveforms were added to every heartbeat of the clean non-VLP records. The offset (ending sample) estimated from the vector magnitude V of the clean non-VLP records was used as a reference to align the VLPs, forcing them to be in the last portion of the QRS complexes. Two different patterns were implemented, one of them with a fixed distance (-5ms) and the other with a variable distance from the reference to the basic VLP waveforms in order to simulate the positional variation due to physiological causes. Therefore, two other groups were created, which will be called here on as clean fixed-VLP and clean variableVLP records. The distance between the VLP waveforms and the reference marks on the

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variable-VLP records follows a normal distribution with -5ms-mean and standard deviation of 0.7ms. 4.5.3 Noisy records According with the published standards [26], the noise in the isoelectric intervals, after averaging between 50 and 300 heartbeats and high-pass filtering (4-pole Butterworth) with a cutoff frequency of 25Hz, should be less than 1µV rms. Averaging a greater number of heartbeats to achieve an adequate noise reduction implies a poor recording. On the other hand, according with Eq. 2.14, after averaging 300 heartbeats, the noise level can be reduced around 17.32 times if the noise is additive, uncorrelated with the signal and stationary. According with analysis detailed in Section 5.5 (see Figure 5.14 and Eq. 5.23), the expected reduction of the noise level by applying the high pass filter with cutoff frequency of 25Hz is 97.8%. This means that in a normal recording, the original noise level cannot be greater than 17.7µV rms. It should be noticed that if the same analysis is performed for the cutoff frequency of 40Hz, with a final noise level allowed of 0.7µV rms [26], and 96.4% of noise reduction, the original noise level should not be greater than 12.6µV rms in an acceptable recording, which is a contradiction in the standards. Taking the above analysis into account, in Chapter 5 the level of noise affecting the HRECG test signals was fixed at approximately 17.7µV rms (noise power of 313.3µV2) to simulate the most severe noise conditions allowed by the standards [26]. A moderately low level of noise was also needed to assess the influence of noise on the algorithms to be evaluated. For this moderately low noise, a value of approximately 7.2µV rms (noise

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power of 52µV2) was adopted. Therefore, in every simulation in Chapter 5, the originally “clean” HRECG signal is available, as well as the signal with a moderate level of noise and the signal with a severe level of noise. In Chapter 6, every clean record (non-VLP, fixed-VLP and variable-VLP) was contaminated with typical ECG noise to obtain the noisy non-VLP, noisy fixed-VLP and noisy variable-VLP records, respectively. The contaminating noise comprises baseline wandering and amplitude modulation (in phase quadrature) due to respiration, and electromyographic (EMG) noise, based on the algorithms proposed in [73].

The

respiration effects were simulated as a 0.2Hz sinusoid with amplitude that is 3% of the ECG maximum peaks.

The EMG noise was synthesised as a coloured (0-300Hz)

Gaussian sequence, with amplitude of 12.6µV rms. It should be mentioned that powerline interference was excluded from these test signals in Chapter 6 to simplify the processing assessment. This did not affect the results because the powerline interference cancellation, in cases of high interference, can be suppressed in the first pre-processing stage. However, typical interference remnants were included in the basic P-QRS-T segments from which all the test records were derived. 4.5.4 Reproducibility assessment One of the objectives of this thesis is to reduce the amount of data needed to conduct a reliable VLP analysis. To achieve the previous objective, five different one-minute records were generated from every one originally collected. This can be useful to assess repeatability of a test. That is, since the five new records are generated from the very

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same patient data, VLP analysis of these records should be expected to yield consistent results. The first (1 of 5) and the last (5 of 5) 1min segments from every 5min record were used to assess repeatability of the algorithms of Chapter 6. In addition, the results with the 1min sequences can be compared with those using 5min sequences to evaluate the effects of using short data segments. For some tests, the five possible records split from every 5min record were used. 4.5.5 Summary To evaluate the algorithms designed in Chapter 5, different combinations of test records were used, based on the rationales explained before. On the other hand, for Chapter 6 algorithm evaluation, the complete set of test signals includes (all records are 3-lead): •

34 records of clean non-VLP signal with length of 5min (c1~c34),

•

170 records of clean non-VLP signal with length of 1min (split from c1~c34),

•

34 records of clean fixed-VLP signal with length of 5min (cVLP1~cVLP34),

•

170 records of clean fixed-VLP signal with length of 1min (split from cVLP1~cVLP34),

•

34 records of clean variable-VLP signal with length of 5min (cVLPj1~cVLPj34),

•

170 records of clean variable-VLP signal with length of 1min (split from cVLPj1~cVLPj34),

•

34 records of noisy non-VLP signal with length of 5min (n1~n34),

•

170 records of noisy non-VLP signal with length of 1min (split from n1~n34),

•

34 records of noisy fixed-VLP signal with length of 5min (nVLP1~nVLP34),

•

170 records of noisy fixed-VLP signal with length of 1min (split from

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nVLP1~nVLP34), •

34 records of noisy variable-VLP signal with length of 5min (nVLPj1~nVLPj34),

•

and 170 records of noisy variable-VLP signal with length of 1min (split from nVLPj1~nVLPj34).

4.6 Summary The commercial HRECG systems available are very expensive, most of them do not fulfil the published standards, and they are not flexible enough to include the new approaches to the VLP analysis. In this work, a PC-based system for VLP analysis was developed to overcome the drawbacks mentioned above. The front-end has 4 channels comprising a low-noise pre-amplifier, an isolation amplifier, and low-pass and high-pass filters. The acquisition block includes a S/H card (DBK17), and a 16-bit A/D conversion card (DaqBoard 216/A), controlled by a LabView customised software (Daq_216A). The following parameters were selected: differential gain Ad = 800 (resolution better than 0.19µV), bandwidth Bw = 0.5-300Hz, and sampling frequency fs = 1kHz. All the algorithms to process the data were implemented as .m files, in MATLAB 5.3 (MATLAB 6.0 compatible), taking advantage of its friendly GUIs, and the flexibility provided. A HRECG database was created with the previously described PC-based system. This database includes the HRECG signal from 59 post-MI patients and 63 healthy volunteers with no evidence of CVD. 5-minute records of the bipolar X, Y, and Z leads from each subject were simultaneously collected. By using the fourth channel of the acquisition

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block, a common mode signal Vcm was recorded to be used as a reference for common mode signal cancellation if necessary. This database was used to test the algorithms implemented in this thesis (including those in this Chapter) in very realistic scenarios. Furthermore, simulations of the HRECG signal, VLPs and noise were designed to evaluate these algorithms in a more controlled environment. Both sources (real HRECG signals and simulations) can be used to assess the performance of general algorithms used in ECG signal processing.

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Chapter 5 - ECG pre-processing algorithms

Chapter 5 - ECG pre-processing algorithms 5.1 Introduction In electrocardiography (conventional and HRECG), previous to the extraction of information from the ECG signal, certain pre-processing is frequently needed. Most ECG machines (electrocardiographs and bedside monitors) include in some way, hardware- or software-implemented, powerline interference cancellation, QRS detection, and high-pass filters. The powerline interference cancellation and the high-pass filtering are normally optional because they may attenuate important components of the signal and introduce significant levels of distortion. The QRS detector is associated with signal averaging or other enhancing techniques, with heart rate computations and with particular algorithms for diagnosis (e.g. arrhythmia detection). In the case of HRECG to analyse VLPs, the restrictions imposed on such algorithms are even more demanding.

The use of powerline interference cancellers has been

discouraged [26] because of the ringing that can be introduced in the region of interest. A similar problem appears after high-pass filtering the HRECG, which may affect the onset and offset of the filtered QRS complex. The IIR high-pass filter proposed by Simson [182] (Figure 1.2) solves this problem, but its ringing affects the central part of the QRS complex, and the corresponding analysis of the abnormal intra-QRS waveforms. On the other hand, the QRS detector should allow an accurate detection of the fiducial marks (trigger jitter < 1ms), rejecting PVCs and very noisy complexes [26]. In this Chapter, novel approaches to the above mentioned pre-processing stages are presented. The first algorithm explained here is an automatic isoelectric interval detector

129


to be used with the new powerline interference canceller. It should be emphasised that, although here these algorithms are targeted to the HRECG pre-processing, they can also be used with conventional ECG recording.

5.2 Isoelectric interval detector For noise characterisation (Section 4.4.2) and to support other algorithms, e.g. powerline interference canceller (Section 5.3), it is useful to isolate the isoelectric segments of the HRECG signal.

In this thesis, an automatic detector of isoelectric intervals was

implemented. This detector is based on the fact that the variance of the signal during the ST and TP segments has a minimum value. To estimate the variance along the sequence, a moving window was used. This window should be long enough to allow obtaining an acceptable variance estimate, but at the same time, it should be relatively short to guarantee that no high slope signal is included in the interval. In this particular database, the sampling frequency was 1kHz and the nominal powerline frequency was 60Hz. The length of the moving window and the step size were fixed both at 50ms (50 samples), which is equivalent to 3 periods of the powerline signal. This ensures that no step discontinuities occur on concatenating of the windows. In addition, the 50ms window is a good compromise to achieving an acceptable variance estimate. Initially, the variance of every 50-sample interval (1-sample step) contained in the first 2second segment of the individual leads was estimated. Then, the minimum variance estimated was accepted to be associated to an isoelectric interval and taken as a reference to look for the only-noise segments. The search for 50-ms isoelectric intervals re-starts at sample 1 and continues till the end with a step size of 50ms. Because of the step size of

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the searching window, some part of the isoelectric intervals may be discarded, but it will be granted that the segments extracted resemble the noise corrupting the HRECG. Figure 5.1 shows an example of the only-noise intervals automatically isolated from the HRECG signal. The square wave represents the transitions between the “isoelectric” (high level) and “non-isoelectric” (low level) intervals. This automatic identification of only-noise segments limits was used in Section 4.4.2.

Figure 5.1 Isoelectric intervals detected automatically (p50, X-lead, 1.2-3.6sec). A visual and analytical characterisation of the noise corrupting the HRECG can be done only from a relatively long sequence. Therefore, to characterise the background noise embedded in the HRECG, a long sequence was obtained by concatenating several isoelectric segments.

Due to the segment size of 50ms, a 20Hz artifact may be

introduced if special attention is not taken.

To avoid the introduction of spurious

components, the first sample of every segment is forced to follow the trend of the last samples of the previous one, thus smoothing the transitions between segments. Due to the natural characteristics of the ST and TP segments, the final composition of the concatenated segments may include a very low frequency component. To be more precise, the composition can be characterised as typical HRECG noise riding on a very

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low-slope ramp. This slowly varying drift is removed, without introducing any filtering distortion, by subtracting the estimated ramps from every concatenated sequence. The isoelectric sub-segments extracted can keep the same position as in the original signal, i.e. not concatenated as needed for noise characterisation. To achieve this pattern, zero level substitutes the non-isoelectric sub-segments. The signal above described is called iso0 and it was used in the novel powerline interference canceller (Section 5.3.2).

5.3 Powerline interference cancellation Several measures should be taken in order to suppress powerline interference in electrocardiography. Unfortunately, it is not always possible to diminish this interference to an acceptable limit during the acquisition process. Appendix D, for instance, shows high levels of powerline interference (and its harmonics) in the data collected. In cases with excessive interference, some cancellation should be performed to avoid discarding the file. However, the published standards for VLP analysis [26] state, “notch filters for powerline interference should not be used.” This recommendation is based on the distortion (filter ringing effect) introduced by the notch filters in the regions of data that change rapidly from higher to lower frequency bandwidths in the direction of filtering after the “discontinuity”. It should be noticed that this is the case of the VLP region following the high-amplitude QRS complex. The ringing effect of the conventional filtering also appears associated with adaptive noise cancelling. However, a new adaptive noise canceller has been implemented to reduce the powerline interference (and its harmonics) without introducing considerable distortion on the HRECG signal. This algorithm was evaluated and showed consistent

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superiority against other more conventional techniques.

Therefore, this optional

operation can be used to enhance individual leads chosen by the user, if required. Nevertheless, this cancellation should not be used if it is not strictly necessary, because of its considerable computational burden. 5.3.1 Conventional and adaptive notch filters The transfer function of a digital notch filter at a frequency fl can be represented as ⎛ f ⎞ 1 − 2 ⋅ cos⎜⎜ 2π l ⎟⎟ ⋅ Z −1 + Z − 2 fs ⎠ ⎝ . H (Z ) = ⎛ f l ⎞ −1 1 − 2 ⋅ r ⋅ cos⎜⎜ 2π ⎟⎟ ⋅ Z + r 2 ⋅ Z − 2 fs ⎠ ⎝

Eq. 5.1

This filter will have a zero on the unit circle at an angle corresponding with fl and a pole at the same angle with a radius of r [86]. Figure 5.2 shows the magnitude response, group delay and impulse response of this notch for a powerline frequency of 60Hz and r=0.98. As r increases, approaching the unit circle, the bandwidth of the notch decreases and the interference can be filtered out without distorting the components of the signal close to fl, however at the same time the ringing effect gets worse. In addition, the centre of a very narrow notch may not fall exactly over the interference frequency, if fl is not precisely known or drifts slowly in frequency. If a reference signal with the interference components is available, an adaptive noise canceller can be implemented, offering easy control of bandwidth, an infinite null, and the capability of tracking the exact frequency and phase of the interference.

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Magnitude Response (dB)


10 0 -10 -20 -30 -40 100

200

300

400

500

Frequency (Hertz) 50

1

40

Amplitude

Group delay (in samples)

0

30 20

Impulse response 0.5

0

10 0 0

200

400

10

Frequency (Hertz)

20

30

40

Time (samples)

Figure 5.2 Characteristics of a digital notch filter with fl=60Hz and r=0.98. In a conventional adaptive filter (Figure 2.10), used as interference canceller, the interference n added to the signal s in the main input of the filter can be modelled as, ⎛ f ⎞ n[k ] = A ⋅ cos⎜⎜ 2π l k ⎟⎟ , fs ⎠ ⎝

Eq. 5.2

⎛ ⎞ f r[k ] = Vcm [k ] = C ⋅ cos⎜⎜ 2π l k + ϕ ⎟⎟ . fs ⎝ ⎠

Eq. 5.3

while the reference signal r is

In Eqs. 3.4 and 3.5, fl is the powerline frequency, fs is the sampling frequency and ϕ is the phase difference between the interference in both inputs. This implies that the reference has the same frequency fl but it may have different magnitude (C instead of A) and phase than the interference n affecting the signal.

W(Z) estimates n from the

reference input, providing magnitude scaling (A/C) and phase shifting (ϕ), which in turn 134


implies that 2 weights (W1 and W2) are needed. This first order FIR filter can be characterised by, W ( Z ) = W1 + W2 ⋅ Z −1 ⎛ W ⎜⎜ ⎝

fl fs

⎞ ⎛ ⎟⎟ = W1 + W2 ⋅ cos⎜⎜ 2π ⎠ ⎝

fl fs

⎞ ⎛ ⎟⎟ − j ⋅ W2 ⋅ sin⎜⎜ 2π ⎠ ⎝

fl fs

⎞. ⎟⎟ ⎠

fl fs

⎞⎞ ⎟⎟ ⎟ . ⎟ ⎠⎠

Eq. 5.4

In the steady state,

⎛ nˆ[k ] = C ⋅ W ⎜⎜ ⎝

fl fs

⎛ ⎞ ⎟⎟ ⋅ cos⎜ 2π ⎜ ⎠ ⎝

⎛ fl k + ϕ − θ⎜⎜ fs ⎝

Eq. 5.5

Taking into account the magnitude scaling and phase shifting which have to be introduced by the filter, ⎛ f ⎞ A ⎛ f ⎞ W ⎜⎜ l ⎟⎟ = = W12 + 2W1W2 cos⎜⎜ 2 π l ⎟⎟ + W22 , fs ⎠ ⎝ fs ⎠ C ⎝

Eq. 5.6

⎛ ⎛ f ⎜ W2 sin⎜⎜ 2 π l fs ⎛ f ⎞ ⎜ ⎝ θ⎜⎜ l ⎟⎟ = ϕ = arctan ⎜ − ⎝ fs ⎠ ⎜ W + W cos⎛⎜ 2 π 1 2 ⎜ ⎜ ⎝ ⎝

Eq. 5.7

⎞ ⎟⎟ ⎠ fl fs

⎞ ⎟ ⎟ ⎟. ⎞⎟ ⎟⎟ ⎟ ⎠⎠

It can be shown that, W2 =

A ⎛ f sin 2 ⎜⎜ 2π l fs ⎝ C⋅ 2 tan (ϕ )

⎛ ⎛ f ⎜ sin⎜ 2π l ⎜ fs ⎜ W1 = −W2 ⎜ ⎝ ⎜ tan (ϕ ) ⎜ ⎝

⎞ ⎟⎟ ⎠ − cos 2 ⎛⎜ 2π f l ⎞⎟ + 1 ⎜ f s ⎟⎠ ⎝

⎞ ⎟⎟ ⎠ + cos⎛⎜ 2π ⎜ ⎝

fl fs

⎞ ⎟ ⎞⎟ ⎟⎟ ⎟ ⎠⎟ ⎟ ⎠

.

Eq. 5.8

This filter is minimum phase as long as the zero lies strictly inside the unit circle (|Z|≤1), where the zero is determined by

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W Z =− 1 = W2

sin(ϕ ) . ⎛ ⎞ fl + ϕ ⎟⎟ sin⎜⎜ 2 π fs ⎝ ⎠

Eq. 5.9

For the case of an LMS adaptation algorithm [87] with step-size parameter µ, the bandwidth Bw and the quality factor Q of the notch, which is a measure of the sharpness of the filter, are given by

µ ⋅C 2 ⋅ fs π π ⋅ fl Q= µ ⋅C 2 ⋅ fs Bw =

.

Eq. 5.10

In a practical situation, not only the powerline frequency, but also its harmonics will interfere with the HRECG (Appendix D). This means that several notches tuned to the harmonic interference frequencies have to be used in order to reduce the complete interference signal [87].

For the adaptive interference cancelling, the number of

coefficients of the filter must be increased as the number of frequency components increases; for instance, to cancel the 60Hz, 180Hz and 300Hz interference components, 6 coefficients will be needed (FIR filter of fifth order). Unfortunately, because of the instrumentation noise and other noise sources, the reference signal will contain other frequency components, which will cause the poles to move away from the unit circle and decreasing the notch depth. Filtering the reference, prior to the adaptive cancellation scheme can circumvent this problem. In this approach, additional reference signals at the appropriate frequencies (powerline frequency and its

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significant harmonics) are derived from the original one. The adaptive cancellation process (with only 2 weights) is then repeated for each of the harmonics to be cancelled.

x[k] = s[k]+n[k]

+ -

Isoelect. detector

^s[k]

+ -

iso0[k]

SW1

S/H S

^n[k]

H

Vcm [k]

W1 W2 RLS

Figure 5.3 New adaptive powerline canceller. 5.3.2 New powerline interference canceller

The new algorithm implemented in this thesis is shown in Figure 5.3. This set-up includes an adaptive first order RLS canceller, which uses the signal Vcm as a reference, as well as the isoelectric interval detector, explained in Section 5.2, to obtain segments that do not contain high-sloped waveforms, i.e. QRS complex and P and T waves. Actually, the isoelectric interval detector yields a signal (iso0) containing the same powerline interference as the original HRECG record (without low-frequency components), during the isoelectric intervals.

However, during the non-isoelectric

intervals the output is zero. The signal iso0 is used as a primary input to adjust the coefficients (W1 W2) of the adaptive noise canceller, controlled by an RLS algorithm, in order to estimate the interference ( nˆ ) from the reference (Vcm).

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This estimated


interference is subtracted from the raw HRECG signal (x) to obtain a “free-interference” signal (ŝ). The adaptation in this system can be inhibited in certain cases by the software switch SW1.

Two states are well defined, one (S/H=1) during which the filter adapts its

coefficients by “sampling” the signal iso0 and minimising the error signal in the meansquare error sense, and the other one (S/H=0) during which adaptation stops and the coefficients are “held”. This last state is associated with the intervals where iso0 is 0, which coincide with the non-isoelectric segments. By stopping the adaptation during these intervals, the ringing effect is avoided. Also, as iso0 does not change abruptly from the end of one sampling interval to the beginning of the next one, because low-frequency components have been removed, discontinuities are eliminated in the adaptation of the coefficients. Despite its higher computational burden, the RLS algorithm was chosen, instead of the LMS, because of its faster rate of convergence. It should be mentioned that the duration of the ephemeral ringing components is partly governed by the rate of convergence of the algorithm. In the case of the LMS algorithm, the convergence rate could be improved by increasing the step-size parameter but the bandwidth of the notch will increase (Eq. 5.10), as well as the stability may be compromised.

To manage certain changes in the

characteristics of the interference, a forgetting factor (λ) of 0.99 was used with the RLS algorithm.

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5.3.3 Evaluation and discussion Performance with real noisy ECG signals

The new adaptive powerline canceller shown in Figure 5.3 was applied to all the raw HRECG signals collected in this thesis (Appendix D) and the enhancement achieved was remarkable. Figure 5.4 shows the estimated PSD of the remaining noise after applying this filtering technique to the same signal (p50, X-lead) whose PSD is shown in Figure 4.8. It can be noticed that the 60Hz, 180Hz and 300Hz components almost disappeared from the enhanced signal, while the rest of the components did not change significantly.

Figure 5.4 Estimated PSD of the noise (p50, X-lead) after filtering.

The global noise power was reduced from 180.3µV2, before applying the filter, to 18.4µV2 (90% of reduction), while the 60Hz component decreased from 123.4µV2 to 1.4µV2 (99% of reduction). The 180Hz component dropped from 7.0µV2 to 0.4µV2 (94%) and the 300Hz component from 0.7µV2 to 0.2µV2 (70%). Now, the general contribution of the powerline frequency and its harmonics (including the alias of the ninth harmonic) to the noise power is only 3.2µV2, which is just a 17.4% of the total.

139


The WC changed from –11.04dB to –3.95dB, while the ESB increased from 4.86Hz to 123.02Hz after applying the new powerline interference reduction technique. Appendix E reviews the same parameters as Appendix D (WC, ESB, the total noise power, and the partial contributions of the powerline frequency and its harmonics for every record) but associated to the filtered signals.

A comparison between these

parameters before and after filtering shows a consistent superiority of the enhanced signal even when several poor quality references were used. It should be noticed that the poor quality of such references was due to data collection irregularities, which can be avoided in future data collection. Tests in a controlled scenario

To test this new algorithm in a more controlled scenario, an experiment was carried out. From the signals included in Appendix E, 13 lead records, with low levels of powerline interference, were carefully selected. Such records with the remaining instrumentation and biological noise are taken as the signal s, to which known amounts of sinusoidal noise was added. Four different levels of interference (n1 to n4), which include sinusoids at the powerline frequency, and its third and fifth harmonics, were added to the signal, s. The powerline frequency was fixed at 59.4Hz to simulate variations that can be present in a practical situation. The interference signals n1 and n2, simulated a high-interference situation, and were composed by adding a 20µV sinusoid at the powerline frequency, a 1.6µV sinusoid at the third harmonic frequency, and a 0.8µV sinusoid at the fifth harmonic frequency. The relative amplitude of the sinusoids contained in the interference were taken from the

140


values obtained in Appendix D, while the absolute values were selected to result in an overall noise power of approximately 200µV2. The low-level interference signals, n3 and

n4, consist of a sum of sinusoids at the same frequencies as n1 and n2, but with amplitudes that are reduced by 40% (power of noise 32µV2). n1 and n3 have initial phase 0 (the same than the reference signal), while n2 and n4 have an initial phase of 0.06π rads. The simulated reference (Vcm) contains the same frequency components as the interference signals, that is, the powerline, third harmonic and fifth harmonic, with amplitudes of 100µV, 10µV and 5µV, respectively. The amplitude values were taken from the results in Appendix D. This reference also includes a random Gaussian noise with zero-mean and 3µV of standard deviation, which simulates the instrumentation noise. Every interference realisation (n1, n2, n3, and n4) was added to the “clean” signal s to obtain noisy realisations sn. Then, the signal was processed by four different techniques, a multi-notch filter (se1), two adaptive interference-cancelling algorithm using LMS (se2) and RLS (se3) adaptation, and the new technique explained above (se4). The first technique consists of a 3-stage multi-notch tuned at 300Hz, 180Hz and 60Hz, applied in that order and calculated by Eq. 5.1 with values of r of 0.999975, 0.9999 and 0.99 respectively. These values of r for the multi-notch were estimated to make it perform close to the cancelling LMS algorithm [87], by using the expression r = 1 − µC 2 ,

141

Eq. 5.11


where C is the amplitude of the reference sinusoid used by the adaptive algorithms and µ is the step-size parameter of the LMS adaptation. The LMS cancelling procedure was implemented with 6 weights to be able to cancel out the 3 sinusoids that constitute the interference. The step-size parameter, µ, was fixed to 0.000001, as a compromise between stability and convergence rate of the algorithm. The conventional RLS procedure was also implemented with 6 weights, and a forgetting factor of 0.99 to admit a certain degree of variation in the interference signal. Finally, the new interference canceller was implemented as explained earlier, by using the new references obtained after filtering the original reference with adequate 4-pole Butterworth band-pass filters applied bidirectionally. Results

Figure 5.5 compares the remaining noise present in the estimated signals by using the 4 different techniques mentioned above. The signal s used here was the filtered X-lead collected from the healthy volunteer 11 (fv11) and the interference was n2. The plots in the figure are limited to the segments of interest around the first 3 fiducial marks (100ms before and 156ms after). The upper plot corresponds to the noisy signal (s + n) and the second plot shows the interference n added to the signal s and which is expected to be cancelled. The third plot represents the remaining interference (θ1) after applying the multi-notch to the noisy signal. The fourth and fifth representations (θ2 and θ3) are associated to the background interference after adaptively cancel it with an LMS and RLS algorithm respectively. It can be seen that the behaviour of all these algorithms is critical close to the high slope

142


segment, around the QRS complex, where certain degree of ringing appears. The bottom plot (θ4) shows the superiority of the new interference canceller, which not only suppresses more effectively the interference but also avoids the ringing effect.

Figure 5.5 Evaluation of interference canceller procedures (X-lead, fv11, n2).

The variance and the bias of the remaining noise after applying each technique can be calculated by Eqs. 2.9 and 2.10, respectively. These parameters allow for analytical evaluation of the interference cancelling techniques. For instance, for the plots in Figure 5.5, the variance of the added interference was 201.62µV2.

This was changed to

161.7µV2 after applying multi-notch, 1520.0µV2 after LMS, 387.8µV2 after RLS and to only 24.5µV2 when the new canceller was used. The initial bias of the noise was 13.1µV, being changed to 9.3µV, 21.5µV, 12.0µV, and 3.9µV respectively, using the four cancellation techniques.

Again the superiority of the new algorithm is clearly

demonstrated. 143


Appendix F reviews the variance and bias of the remaining noise for every estimated signal in this experiment, the clean signal s and the noisy signal sn. In addition, it includes the features extracted from the VLP analysis in the time domain (Simson test), illustrating that the new canceller, unlike the other methods, does not affect the results of the Simson test.

20 Bias (µV)

2

Variance (µV )

1500

1000

15 10

500

5 0 sn

notch LMS RLS Algorithm

nRLS

sn

nRLS

160

8

QRSd (ms)

noise (µV rms)

10

notch LMS RLS Algorithm

6 4

140 120 100 80

2

60 40

0 sn

notch LMS RLS nRLS clean Algorithm

sn

notch LMS RLS nRLS clean Algorithm

Figure 5.6 Evaluation of powerline cancellation algorithms (review of Appendix F).

Figure 5.6 reviews some results included in Appendix F for the severe levels of noise (n1 and n2) by using notch-box and whisker plots [129]. In this kind of plots, the boxes have lines at the lower quartile, median, and upper quartile values; the whiskers extend from each end of the box to show the extent of the rest of the data; the outliers (data with values beyond the ends of the whiskers) are marked with +; and the notches represent a

144


robust estimate of the uncertainty about the means for box to box comparison. It can be seen that the variance of the noisy signal (sn) is considerably and consistently diminished by the new powerline-cancelling algorithm (nRLS), contrasting with the performance of the other algorithms.

Feature

QRSd

LASd

RMS40

Estimations (correlation with value from s; p-value) se1 se2 se3 se4 sn all cases (n1~4) 0.910; 0.000 0.52; 0.000 0.226; 0.107 0.492; 0.000 0.983; 0.000 extreme (n1~2) 0.888; 0.000 0.524; 0.006 0.226; 0.267 0.491; 0.011 0.977; 0.000 moderate (n3~4) 0.950; 0.000 0.517; 0.007 0.226; 0.267 0.492; 0.011 0.990; 0.000 all cases (n1~4) 0.849; 0.000 0.530; 0.000 0.389; 0.004 0.314; 0.023 0.970; 0.000 extreme (n1~2) 0.813; 0.000 0.528; 0.006 0.389; 0.049 0.314; 0.118 0.963; 0.000 moderate (n3~4) 0.916; 0.000 0.531; 0.005 0.389; 0.049 0.314; 0.118 0.979; 0.000 all cases (n1~4) 0.408; 0.003 0.171; 0.226 0.390; 0.004 0.124; 0.383 0.855; 0.000 extreme (n1~2) 0.243; 0.231 0.176; 0.389 0.390; 0.049 0.124; 0.547 0.813; 0.000 moderate (n3~4) 0.667; 0.000 0.166; 0.419 0.390; 0.049 0.124; 0.547 0.904; 0.000 noise

Table 5.1 Correlation coefficients (and p-values) between the features from the clean signal (s) and the noisy (sn) and estimated signals (se1~4)

To determine the linear relationship between the features extracted from the clean signal and from the noisy and estimated signals, the Pearson correlation coefficients were determined, assisted by Minitab 13.31 (Minitab Inc., www.minitab.com). Table 5.1 shows the Pearson correlation coefficients and the p-values found, with a clear superiority for the se4, i.e. the signal estimated by the new adaptive powerline enhancer. Therefore, the new algorithm also shows its superiority for the feature extraction (QRSd, LASd, RMS40), allowing estimations linearly related to those with the “clean” signal. However, this procedure does not improve significantly the results in the time domain analysis compared to those obtained directly with the noisy signal sn when the original level of interference is moderately low (n3 and n4).

Therefore, this new adaptive

interference canceller, which is a time consuming procedure, should not be used for the

145


conventional time domain analysis when the interference is not easily appreciated in the original record. It should be emphasised, however, that this set-up allows using data collected in non-optimal conditions in a non-shielded room.

5.4 QRS detector The QRS detector is the cornerstone of several algorithms used to enhance the SNR. It is crucial in the coherent averaging technique and in the segmentation of the ECG signal. The standard method [26] to align the heartbeats s(t) in the presence of noise n(t) is matching the waveforms against a template of averaged beats ŝ(t). The impulse response

h(t) of this matched filtering is given by

h(t ) = sˆ( −t ) .

Eq. 5.12

Accordingly, the filter output is given by

y[k ] = x[k ] * sˆ[ −k ] =

∞

∑ x[k ] * sˆ[−(m − k )] = φ xsˆ [m] ,

Eq. 5.13

k = −∞

which means that this convolution of the noisy signal (x[k]=s[k]+n[k]) with the reversed sequence of the template (ŝ[-k]) can be computed as a cross-correlation. If the corrupting noise is white noise, the fiducial marks for alignment coincide with the maximum SNR at the sampling instant, which is the solution of d [(s(t ) + n (t ) ) * h (t )] =0. dt

Eq. 5.14

It should be emphasised that this matched filter is optimum if the PSD of n(t) is constant in the frequency range of s(t), i.e. white noise.

However, its performance can be

seriously affected by the powerline interference [106]. In this new PC-based system, a

146


double-level algorithm is used to implement a QRS detector. An optional matched filter algorithm can then be used to provide a fine adjustment feature. 5.4.1 Enhanced double-level algorithm

The enhanced double-level (EDL) algorithm (Figure 5.7) includes a pre-processing stage that starts with the selection of the reference channel. Any individual lead (X, Y or Z) or a composite signal (C), with information from all of them, can be used as a reference for the QRS detector. In the case of using X, Y, or Z as a reference, the QRS complex (positive or negative) should be well defined, easily differentiable from the P and T waves, and with high SNR. Since it is not always easy to determine the best individual lead to be used as a reference channel, the composite signal C, which represents a good compromise for the QRS detection process although increasing complexity, is adopted as a default reference in this system. The composite signal is obtained by adding the positive part of every preprocessed single lead (after high and low-pass filtering). After selecting the reference channel (or before in the case of C), the QRS complex components, centred around 17Hz [71], are emphasised, which is a modification to the classic double-level algorithm [106]. First, the reference signal is high pass filtered with a zero-phase forward and reverse first order Butterworth filter with a cutoff frequency of 9Hz to remove low-frequency noise such as the baseline wandering and to diminish the components of the P and T waves (2-3Hz). Then, a zero-phase forward and reverse second order Butterworth filtering is applied as a low pass filter with a cutoff frequency of 32Hz to diminish the 60Hz interference and high frequency noise. The use of the

147


Butterworth filtering in the forward direction and then reversing the filtered sequence and running it back through the filter avoids shift on the QRS complexes due to phase distortion.

Pre-processing: Selects reference channel (±X, ±Y, ±Z, C) High pass filter (fc = 9Hz) Low pass filter (fc = 32Hz) Initial threshold (2sec) at 50% of peak Advance sample Next crossing points, t1 & t2

no

yes min30) of the

6

To be precise, the finite sampling frequency (fs) introduces a misalignment that is uniformly distributed between ±(1/2fs). Accordingly, the associated standard deviation σ of the misalignment is given by 0.289/fs [192]. 153


random variable τ were taken, which should be sufficient to achieve a statistically accurate value [54]. Performance with noisy ECG signals

Appendix G and Figure 5.11 review the results obtained in the evaluation of the EDL and the CCA affected by different levels of Gaussian white noise (n3 and n4) and powerline interference (n1 and n2). As expected, the CCA worked consistently better than the EDL algorithm; and higher levels of noise and interference (n4 and n2) affected the performance of the algorithms in a more serious way. However, contrary to previously reported in [106], the powerline interference (n1 and n2) did not cause as poor a performance as the white Gaussian noise (n3 and n4, resembling the characteristics of the EMG and instrumentation noise) of the same power. This behaviour is preferable since the powerline interference is the most common noise in the clinical environment [71]. In addition, the improvement of the alignment after cross-correlation adjustment is more significant in the presence of the powerline interference compared with the white Gaussian noise. Occasionally, several heartbeats were discarded, mainly in the presence of n4, because the cross-correlation coefficient between the heartbeat and the template was below 98%, meaning that the level of noise was above the acceptable limit. Even for the worst cases, the trigger jitter [26] was below 1ms and in most cases was lower than 0.5ms, which has no serious consequences on the averaging process.

154


standard deviation (ms)

0.8 60Hz, EDL 60Hz, CCA EMG, EDL EMG, CCA

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10

15

20

25

30

35

40

SNR (dB)

Figure 5.11 Performance of the algorithms at different SNRs.

Table of Appendix G includes the signal-to-noise ratio (SNR) estimated as P SNR = 10 ⋅ log10 s , Pn

Eq. 5.20

where Ps is the power of the clean signal (before adding the noise) and Pn is the power of the noise added (50µV2 for n1 and n3, and 300µV2 for n2 and n4). While the performance of the algorithms has a clear degradation at lower SNRs for the same waveform and type of noise (Appendix G), this trend is not shown in Figure 5.11, where the results using different waveforms are plotted together. This suggests that results strongly depend on the waveforms, specifically on the lead used as the reference channel. Consequently, no comparisons with previous studies [106] [71] [192] [171], which use different waveforms, can be done in an objective manner.

155


Influence of the reference channel

To evaluate the influence of the reference channel (X, Y, Z or C) on the QRS detector algorithms [192] in a realistic scenario, a group of 80 XYZ files were selected from the collected database (Appendices B and C). The selection was based on gathering a large variety of waveforms, while discarding highly corrupted files, e.g. “leads off” situation. Then, the fiducial marks were estimated by the algorithms implemented, using every possible reference channel, and the sequences tX, tY, tZ and tC were obtained. By keeping the same reference channel, the rest can be compared by using the random misalignment between the common reference channel and the rest of them. For instance, with X as a reference, the performance of the algorithms with the channels Y, Z and C as references can be measured up by means of the standard deviations of the relative misalignments σXY, σXZ and σXC, respectively.

However, it is more convenient for

comparison purposes to have the individual channel misalignments effects. Following the same reasoning than for obtaining Eq. 5.19, the variances of the relative misalignments involving two different channels can be written in a matrix format as ⎡σ 2XY ⎤ ⎢ 2 ⎥ ⎡1 ⎢ σ XZ ⎥ ⎢1 ⎢ σ 2 ⎥ ⎢1 = ⎢ XC 2 ⎥ ⎢0 ⎢ σYZ ⎥ ⎢0 ⎢ σ 2 ⎥ ⎢0 ⎢ YC ⎥ ⎣ 2 σ ⎣⎢ ZC ⎦⎥

1 0 0 1 1 0

0 1 0 1 0 1

156

0⎤ ⎡ σ 2 ⎤ 0⎥ ⎢ X2 ⎥ 1⎥ ⋅ ⎢ σ Y ⎥ . 0⎥ ⎢ σ 2 ⎥ 1⎥ ⎢ 2Z ⎥ 1⎥⎦ ⎢⎣ σ C ⎥⎦

Eq. 5.21


σXY2, σXZ2, σXC2, σYZ2, σYC2 and σZC2 are the variances of the relative misalignments between the channels specified in the subscripts, and σX2, σY2, σZ2 and σC2 are the variances of the individual channels. The variances of the relative misalignments can be computed by estimating the standard deviation of the associated misalignments (Eq. 5.21). For instance, σXY2 can be estimated from a sufficient number of samples of the random variable τXY = tX - tY. After computing the variances of the relative misalignments, the variance of the individual channel misalignments can be estimated. This estimation was done by Gaussian elimination in the least square sense to the over-determined system (6 equations and 4 unknowns) of Eq. 5.21. The SNR of every XYZ lead was estimated for the 80 files originally collected (rX, rY and rZ) and its filtered versions after interference cancellation (fX, fY and fZ), as

P − Pnˆ , SNR = 10 ⋅ log10 x Pnˆ

Eq. 5.22

where Px is the power of the noisy signal and Pnˆ is the power of the estimated noise extracted from the isoelectric segments. This SNR is included in Appendices H and I. Appendix H also contains the standard deviations of relative misalignments (σXY, σXZ,

σXC, σYZ, σYC and σZC) along with the estimated standard deviations of the individual misalignments (σX, σY, σZ and σC) and the minimum number of heartbeats (Nmin) obtained with the EDL for the 160 data files. Appendix I reviews the same parameters for the 160 data files but obtained after the CCA.

157


Results

Figure 5.12 displays a notch-box and whisker plot for the SNRs estimated at every lead, the raw data leads (rX, rY and rZ) and the filtered leads (fX, fY and fZ). It can be seen that the SNR of the different leads has similar values between certain limits, although the Z-lead is slightly better, followed by X. After powerline interference cancellation, the SNR improves by approximately 5dB for every lead.

45

SNR (dB)

40 35 30 25 20 15 10 rX

rY

rZ fX Reference channel

fY

fZ

Figure 5.12 Signal-to-noise ratio of the signals included in the study.

The notch-box and whisker plot of Figure 5.13 shows that, despite of the differences in the SNR, the performance of the algorithms by using any of the individual leads XYZ as reference channels is very similar. In the PC-based system, the user can select the reference channel, but in several subjects, it is not obvious to predict which reference channel will give the best results.

158


Standard deviation (ms)

EDL

CCA

1.4

1.4

1.2

1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0

rX rY rZ rC fX fY fZ fC Reference channel

rX rY rZ rC fX fY fZ fC Reference channel

Figure 5.13 Performance of the algorithms with different reference channels.

As an average, the composite channel C is the one that reaches better performance, although with the EDL it does not outperform the rest of the channels as much as it does with the CCA. The CCA consistently yields better results than the EDL alone, although there may be a few exceptions. Although the SNR increases an average of 5dB after the interference cancellation, the algorithms produce almost the same results according with the standard deviation of the misalignments, because it is not very sensitive to the powerline interference, as it was suspected in the previous simulations. The crosscorrelation adjustment may discard a significant number of heartbeats for being considered grossly noisy, but after powerline interference cancellation, less fiducial marks are ignored. It is useful to view this work on QRS detection in the light of previous published work, however there are many factors that make comparison difficult. In [106], although the 159


qualitative effect of the powerline interference was mentioned, no quantitative evaluation was performed. The simulations (or semi-simulations) use only one waveform (200msQRS) repeated 80 times, or eighty 200ms QRS complexes isolated from 6 patients. In [71], the sampling frequency was 4kHz; the levels of noise were excessively high (15100µV rms); there is no reference to the SNR in the simulations and the same QRS complex was repeated three hundred times to generate the test signal. In [192], 64 beats from 12 healthy volunteers were used, but there is no reference to the SNR or levels of noise, while in [171], the signal from 5 healthy volunteers and 4 patients were contaminated with insignificant levels of white Gaussian noise (0.1-10µV rms). Despite of these differences, the averaged results presented here with the EDL and the CCA, under more arduous conditions, are similar or better than those previously reported for this kind of algorithm.

5.5 High-pass filter 5.5.1 Enhanced Simson approach

A high-pass filter (HPF) is used in the VLP analysis in order to reduce amplitude of the QRS complex and attenuate low-frequency components (< 10Hz) of background noise (slow drift of the ST segment). The most frequently used HPF in the VLP analysis is the one proposed by Simson [182] and it has been accepted as a standard [26]. This filter is a 4-pole Butterworth HPF applied in the forward direction until a reset point into the QRS complex, then in the backward direction, from the end of the analysis window up to the same reset point. With the Simson filter, the ending points of the QRS remain at the same position in the filtered signal (see Figure 2.11). In addition, due to the reset point being within the QRS complex, ringing will occur within this segment. 160


The reset point proposed by Simson is placed 40ms after the onset in the forward direction (from left to right) [182]. Therefore, when the duration of the QRS (QRSd) is less than 80ms, which is very common, the estimation of the root mean square value of the last 40ms (RMS40), may be affected by this discontinuity. To avoid such a problem, this PC-based system uses a reset point for the Simson filter at 20ms from the onset. Displacing the discontinuity in the filtering process makes the estimation of the time domain features (Section 2.4.1) more unlikely to be affected. In the PC-based system, before performing any kind of high-pass filtering, the value of the first sample of the signal to be filtered is forced to zero by subtracting from the signal a DC level equivalent to the value of the first sample. In the case of the Simson filter, the procedure is repeated in both directions. With this technique, the edge effect is avoided in the analysis window, without introducing any extra distortion, and therefore, the analysis window can be limited exactly to the region of interest around the QRS complex. The 4-pole Butterworth (Figure 5.14) used in the Simson technique has a sharp frequency response and effectively reduces the noise. Assuming a white Gaussian noise affecting the HRECG, it can be deduced that its standard deviation after filtering is reduced by a factor given by att =

A2 , A1 + A2

Eq. 5.23

where A2 and A1 are the areas below the magnitude response |H(f)|, and between this plot and a pass-all filter (|H(f)|=1), respectively, as shown in Figure 5.14. In the case of the 4pole Butterworth HPF with a cutoff frequency of 40Hz, the attenuation factor is 0.96; while for a cutoff frequency of 25Hz, is 0.97.

161


4-order Butterworth, fc=40Hz

Magnitude response

1 0.8 A1

A2

0.6 0.4 0.2 0

0

50

100

150

200

250 300 Frequency (Hz)

350

400

450

500

Impulse response 1

40 Amplitude

Group delay (in samples)

50

30 20

0.5

0

10 0

0

100

200 300 Frequency (Hertz)

400

-0.5

500

0

10

20 Time (samples)

30

Figure 5.14 Magnitude response, group delay and impulse response of the 4-order Butterworth high-pass filter with cutoff frequency of 40Hz.

However, the Simson filter introduces distortion due to its non-linear phase characteristic especially around the cutoff frequency. To preserve the morphology of the signals of interest inside the whole QRS complex (abnormal intra-QRS waveforms), several authors [82] [113] have suggested certain FIR filters as an alternative to the Simson technique. FIR filters are inherently linear phase and need only be applied in one direction. 5.5.2 FIR filters

There are several FIR filter design techniques described in the literature [145] [100] and implemented as MATLAB functions, which have been used in VLP detection. To reduce the transition band of these filters and obtain a sharp frequency response, a high order is needed, but at the same time, a significant widening of the QRS complex is introduced,

162


associated to certain ringing, which may mask the VLP activity. In addition, most of these filters have ripple in the pass-band and/or stop-band. 5.5.3 High-pass filter implementation

In this work, a different approach was taken to design a flat FIR high-pass filter that introduces an insignificant widening, almost without ringing, while considerably attenuating the low-frequency components (5, the value of k decreases as d increases, and after certain value, the significance of decreasing k is higher than that of increasing d in Eq. 6.7. Testing with different initial noise levels σiso and different number of “heartbeats” N, it was found that the values of d minimising σo were independent of such parameters. Therefore, a value of d = 10 was taken as a default for the MSA (Eq. 6.4) here designed. This default value (d = 10) assures an adequate noise reduction in the isoelectric segment, while avoiding an excessive edge effect. The edge effect occurs around the transition zone between the isoelectric segments and the filtered QRS, i.e. close to the onset and offset, and can affect the estimation of the QRS limits. Fortunately, for d = 10, the effect is not significant. It can be found from Figure 6.8 that for the default value of d = 10, the correspondent value of k is approximately 0.48. The noise power on the isoelectric segment will be attenuated about (2d+1)k times more than using the classical coherent averaging with N heartbeats.

Similarly, to obtain

comparable noise power reduction, the MSA requires a number of heartbeats that is around (2d+1)k times smaller than the classical coherent averaging. From the default values assumed above (d = 10 and k = 0.48), it should be expected that the MSA reduced the noise power approximately 10 times more than the classical coherent averaging, for the same number of heartbeats N. Figure 6.9 compares the noise attenuation achieved by the MSA with d = 10 and by the classical coherent averaging followed by FIR filtering of order 80, for different values of N. Logarithmic plots were used to distinguish easily that the ratio of about 10 between the variances of the output noise for the coherent averaging and the MSA was kept,

190

Chapter 6 - VLP processing techniques

independently of N.

This means that the MSA with d=10 provides a power noise

attenuation of approximately 10dB more than the coherent averaging in the isoelectric segment. For example, with only 32 heartbeats, the MSA can reduce the noise in the isoelectric segment to less than 0.6µV rms, while the coherent averaging (followed by FIR filtering of order 80) needs more than 320 heartbeats to achieve similar performance.

-1

10

coherent ave. MSA, d=10

normalised output variance

-2

10

-3

10

-4

10

2

10

Number of heartbeats, N

Figure 6.9 Values of variance σo2 versus number of heartbeats N.

The MSA may attenuate peaks in the presence of misalignments, like any other averaging technique. However, it exhibits an average performance regarding detail preservation.

191


6.2.4 High pass filtering options The next stage in the signal-processing scheme is the high-pass filter (HPF). The (MSA) averaged leads ( X , Y , and Z ) are high-pass filtered by using the type of filter (f. type) and the cutoff frequency (fc) chosen by the user. The recommended 25Hz and 40Hz [26], as well as 80Hz and 100Hz, are the options for the cutoff frequency. The filter of choice can be the bi-directional Butterworth proposed by Simson [182] and accepted by the standards [26], with the few modifications introduced in Section 5.5.1. The other filter type available in this PC-based system is the one designed and evaluated in Sections 5.5.3-5.5.4, which should be applied before the MSA. Then, the vector magnitude V is computed, as an RMS summation of all leads. 6.2.5 Flexible analysis This new system offers the possibility of individual lead analysis (X, Y and Z) as well as the standard one, with V, at the request of the user. The limits (onset and offset) of the filtered QRS under test are automatically detected by the method suggested in [26] (Section 2.4.1), but the user has the option to verify this by visual inspection and to apply corrections manually if needed. This is done by simply dragging the associated vertical lines in the analysis window. This type of manipulation within the analysis window of the PC-based system offers great flexibility to the user. The values shown in Figure 6.10 are the defaults that are suggested in the standards [26]. However, the user can perform different analysis with different sets of parameters to obtain a more reliable diagnostic measure.

192


Figure 6.10 Analysis window of the PC-based system (fp16, V). 6.2.6 Presentation of the results Once the onset and the offset of the filtered QRS complex are detected, the standard time domain features (QRSd, LASd and RMS of the segment T specified, which is 40ms by default) [26] are extracted and the RMS noise level is estimated in a 50ms isoelectric segment. Then, the filtered QRS complex is plotted and the results are shown in the analysis window of the PC-based system. A colour code is used in this system to help in the analysis of the results. Every feature is compared with the associated threshold selected by the user and, if it is surpassed, the associated background becomes green, like in the case of the LASd of the example because (LASd=49ms) > (LASdmin=38ms), and the case of the RMS40 because

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(RMS40=2.1µV) < (RMS40max=20µV). Similarly, the associated background turns yellow if the threshold is not reached but the value is close enough to it (95% for QRSd, 90% for the LASd and 85% for the RMS40). The normal parameters, that is, those associated with subjects without VLPs, are shown with a white background.

The

foreground of the box showing the noise level will be coloured red if the noise level is excessive (>1µV at fc=25Hz, or >0.7µV elsewhere) as a warning that the results may be in error [26]. 6.2.7 Modified signal averaging versus coherent averaging The coherent averaging combined with a FIR high-pass filter of order 80 (Section 5.5.3) was compared to the MSA preceded by identical filter.

The MSA estimated the

background noise level of every record (σiso) from the isoelectric segment of the first high-pass filtered heartbeat. Then, the MSA fixed the trimming parameter q at 2σiso and the number of displacements d at 10. Variation of parameters at different SNR A Monte Carlo experiment was designed to compare the MSA and the coherent averaging at different SNR levels in the VLP region. The X-lead records of the test signals cVLP15 and cVLPj15 were used as base records. Several levels of noise were added to these base records to obtain different SNR levels in the VLP region. For every SNR, between –6 and 12dB with a step of 3dB, 100 independent realisations were created. From every realisation, several parameters were estimated, and the average of the 100 realisations was taken as the most probable value of such parameter.

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The parameters estimated for this evaluation include the variance and the bias in the VLP region (Eqs. 2.9 and 2.10, Section 2.3.1) and the RMS value in the isoelectric segment of the absolute value of the output signal. In addition, the difference, in dB, between the variance in the VLP region and the variance in the isoelectric segment was computed to assess the contrast between these two regions allowing VLP detection.

This last

parameter indicates the “SNR” of the output signal without taking into account the distortion introduced by the averaging. Figure 6.11 presents the results of the MSA versus coherent averaging comparison (each combined with a FIR filter of order 80) for 60-heartbeat records. Every plot compares the performance of the MSA and the coherent averaging with fixed-VLP (no time jitter) and variable-VLP (random jitter with σ = 0.7ms) records at different SNR levels in the VLP region. In general, the variance and the bias in the VLP region, along with the RMS noise in the isoelectric segment, tend to decrease for higher SNR in the VLP region of the input signal. The difference between the variances in the “VLP” and the isoelectric region (VLP-ISO), however, increases with the SNR of the input. Although the difference tends to be less at higher SNRs, for the fixed-VLP records, the output signal of the conventional coherent averaging has lower variance and bias than the output of the MSA algorithm. However, in a more realistic scenario in which the position of the VLPs vary (variable-VLP records), the variance and the bias increase considerably, but the difference between the coherent averaging and the MSA is less significant. In other words, the MSA performance with regard to variance and bias is always poorer than that of conventional ensemble averaging, provided there is no jitter in

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the position of the VLPs. However, in a real situation, where some time variations are present in the VLPs, the MSA performance is comparable to that of coherent averaging.

40

20

10

0

output isoelectric noise (uV rms)

output bias (uV)

30

6 4 2

-5

0

0 5 10 SNR in the VLP region (dB)

-5


-5


2.5 fixed-VLP, coherent ave. fixed-VLP, MSA with d=10 variable-VLP, coherent ave. variable-VLP, MSA with d=10

2

output VLP-ISO difference (dB)

output variance (uV2 )

8

40

30

1.5 1

20

0.5

10

0

-5


Figure 6.11 MSA versus signal averaging (each combined with FIR filtering, M = 80) for N=60.

The most remarkable advantages of the MSA method over the coherent averaging are based on its superior performance with regard to noise reduction in the isoelectric segment. The bottom right hand plot in Figure 6.11 shows that the difference VLP-ISO is always higher after applying the MSA algorithm. It is also evident that, in these simulations, the variable-VLP records suffer a degradation of more than 6dB because of the low-pass filtering effect due to the VLP misalignments after applying the coherent averaging. For example, from a 0dB input record, the coherent averaging obtains a signal

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with a VLP-ISO difference of 17.4dB (equivalent to 17.4dB enhancement) when the VLPs have constant position, while reducing to 10.7dB in the presence of VLP misalignments. This degradation of more than 6dB is almost independent of input SNRs for the coherent averaging. However, with the MSA this difference is considerably less, especially at low values of SNR. It was found, that the VLPs could be easily identified when the VLP-ISO difference is higher than 20dB. From the correspondent plot in Figure 6.11, it can be concluded that the coherent averaging can detect fixed-VLPs from a 60-heartbeat record when the original SNR is just higher than 3dB, but it needs more than 10dB in the original signal to discover the variable-VLPs. Contrasting with this, the MSA can find VLPs (fixed or variable) from any original record with a SNR greater than -1dB in the VLP region. Variation of parameters at different N Another Monte Carlo experiment was designed to compare the MSA and the coherent averaging, this time at different number of heartbeats, N. The same basic records as above were used. The SNR level in the VLP region was fixed at 0dB. For every value of N, between 32 and 320 with a step of 8, 300 independent realisations were created and the same parameters as before were estimated. Figure 6.12 compares the performance of the MSA and the coherent averaging with fixed-VLP and variable-VLP records for different number of heartbeats available. For the fixed-VLP records, the variance and bias in the VLP region do not change significantly with the number of heartbeats averaged. Similar behaviour is associated with the variable-VLP records when the number of heartbeats is large enough (N>150).

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The coherent averaging assures lower values of variance and bias than the MSA for a particular number of heartbeats, but the difference is less significant in the presence of variable-VLPs. It should be noticed that for this kind of variable-VLP records, which are more indicative of the real-life situation, the variance and bias considerably decreases for N 100. The improvement between the VLP-ISO differences after coherent averaging and MSA is notable for the fixed-VLP records (~4dB), but is even more remarkable for the variable-VLP records (~9dB).

6.3 Adaptive enhancer plus MSA for beat-to-beat VLP detection An alternative time domain analysis strategy for beat-to-beat VLP detection, based on adaptive line enhancing (ALE) plus MSA, was designed. For VLP detection, ALE alone may not be good enough [137]. However, combining ALE and MSA, good results have been obtained with less than 64 beats, even for extreme noisy conditions [202]. The initial ALE + MSA prototype was analysed and improved. 6.3.1 Initial ALE + MSA prototype ALE followed by a MSA was proposed, for VLP detection in [202]. The VLP detection system, shown in Figure 6.13, used a 50-beat HRECG signal as an input. This signal, sampled at 1kHz (fs = 1), was pre-processed to produce a series of records using the QRS peak as a time reference or fiducial mark. The fiducial marks, ta’, were obtained by the QRS detector of Section 5.4. Segmentation of this signal was performed to produce 250ms segments around sample ta’, between ta’ -100fs+1 and ta’ +150fs (fs expressed in kHz). The primary input to the ALE filter can be considered as a 1×(50 · 250 · fs) vector, y:

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y = [ y1,1

y1,2 ... y1,250 fs

y 2,1... y 2,250 fs ... y50,250 fs ] ,

Eq. 6.7

where: is the j-th amplitude sample from the i-th heartbeat, therefore is the fiducial mark sample (ta’).

yi,j yi,100fs

ALE

a

y=x+n

W1…10

Z+250fs

MSA

e

LMS

+

-

r

Figure 6.13 Adaptive line enhancing plus modified signal averaging [202].

For the ALE filter, the reference-input was the vector y, while the primary-input r, was a one-beat advanced version of y, r = [ y 2,1

y 2,2 ... y 2,250 fs

y3,1... y3,250 fs ... y51,250 fs ] .

Eq. 6.8

An LMS algorithm, with order M=10, empirically obtained, was used as the filter adaptation mechanism. The step-size parameter, µ, was determined as a function of the filter order M and the power of the first 250ms heartbeat segment, as

⎛ M 250 fs ⎞ 2⎟ µ = 0.07 ⎜ y ≈ 10 − 7 . ⎜ 250 fs ∑ 1, j ⎟ j =1 ⎝ ⎠

Eq. 6.9

Using this approach, it was concluded that the acquisition time can be reduced five-fold to approximately one minute, while maintaining standards in noise reduction for VLP analysis [202]. This conclusion was reached after evaluating the system with a set of 200


semi-simulated signals and a reduced set of real HRECG signals. However, in a more complete evaluation, increasing the number of real HRECG signals, some limitations of this prototype system became apparent. 6.3.2 Limitations of the initial ALE + MSA prototype

The constant of 0.07 affecting the whole expression in Eq. 6.9 had been adjusted to yield an acceptable value µ for most signals, after a statistical study that took into account the power of the QRS complex respect to the power of the windowed heartbeat. With this constant, µ was low enough to avoid instability at expense of a slower adaptation convergence. Even though, for some real HRECG signals from the database (Section 4.4), the system caused troublesome ringing inside the QRS due to instabilities. The concatenation of consecutive windowed heartbeats may introduce discontinuities on the ALE input, due to different levels of the PQ and ST segments in the vicinity of the QRS complex. These discontinuities may cause instability in the algorithm, introducing ringing on the output signal. In addition, the same effect may appear associated to the abrupt transitions of the QRS complex. Following the ALE filter (Eq. 6.11), MSA (Eq. 6.2) was employed to reduce the variance of the output a. The drawbacks associated with this procedure were explained before, in Section 6.2.3. Consequently, a new adaptive enhancer was devised in an attempt to overcome these limitations. 6.3.3 New adaptive enhancer with modified signal averaging

In the new enhancer, the MSA was initially computed to obtain a good quality reference for the adapter enhancer, whose main mission was not to enhance the signal but to track

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small changes, otherwise lost in the averaging process. This gives certain information on the VLP beat-to-beat variability that can help in the diagnosis. This system, shown in Figure 6.14, forms a matrix x by windowing the data stream around the fiducial marks ta’, i.e. taking lsa samples from the left and rsa samples from the right of the N marks detected by the QRS detector (see Figure 2.6 and Eq. 2.8 in Section 2.3.1). lsa was fixed to 100fs-1, while rsa was fixed to 156fs, with fs=1kHz; therefore, the matrix x has N rows and 256 columns. It should be mentioned that the matrix x includes lead normalization (Section 6.2.2) to reduce respiration effects. Given the matrix x, the standard deviation of the background noise (σiso) can be estimated to perform the MSA (Section 6.2.3), obtaining the output vector y. The matrix x can be developed directly from the acquired HRECG data stream (s+n), but the previous use of a FIR high pass filtering is highly recommended. This early filtering allows a better performance of the adaptive algorithms by diminishing the dynamic range of the input signals, attenuating the drift within the isoelectric segments and enhancing the SNR in general. In addition, by using the FIR high pass filter of order 80, designed in Section 5.5.3, the baseline wandering almost disappears and the segments PQ and ST become levelled, avoiding any sharp transition in the further concatenation process. Due to the steep transition between the large QRS complex and low level VLPs, it was “conjectured” that filtering from the end of the data toward the beginning would give better results. Consequently, a time reversed or “flipped” filtering scheme was adopted.

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HPF FIR M=80

s+n

windowing 1×l

ta’-lsa ~ ta’+rsa

ta ’

&

1×N

lead normalization

1×l

QRS detector lsa=100fs-1 rsa=156fs

x

N×(lsa+rsa+1)

σi

MSA

d

y

m2v & flipping

i

v2v & flipping

r

1×(lsa+rsa+1)

1×(lsa+rsa+1)N

RLS ρ=0.95 r

w1 w2

o1

Flipping 1×(lsa+rsa+1)N

i

+

-

v2m o2

N×(lsa+rsa+1)

MAV

o3

1×(lsa+rsa+1)

Figure 6.14 New adaptive enhancer with modified signal averaging.

The m2v (matrix-to-vector conversion) and flipping block yields the main input (i) and the reference (r) for the adaptive enhancer. To form the vector i, the m2v concatenates

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the N rows of x consecutively and the resultant vector is time reversed. Vector r is obtained by repeating N times the vector y and flipping it over.

By flipping the

concatenated-vectors over, the HRECG sequence is processed in the backward direction. This processing from left to right achieved better stability (less ringing and distortion), and good tracking of the VLP beat-to-beat changes. A second-order RLS adaptive scheme, with a forgetting factor of 0.95, was used to “enhance” the signal i with the reference r. The adaptive enhancer here does not reduce noise in the isoelectric segment compared to the reference r, but it detects certain changes in the VLP segment. It should be mentioned, to be precise, that the system cannot follow every change in i because of the limitations of the reference r, but it gives a good idea of the variability. The RLS algorithm allows a faster adaptation to any variation in the signal.

This

algorithm is more sensitive to noise than the LMS for example, but this is not a problem at the typical SNR (>1) of the input signals. By using a forgetting factor λ of 0.95, the data in the distant past are forgotten [87] and the enhancer can cope with a certain degree of non-stationarity. A filter of order two was found as a good compromise to provide an acceptable frequency separation (long enough), with a quick convergence and low computational load (short enough). It was found that the algorithm converged during the first windowed heartbeat. This second-order enhancer can track not only amplitude variations, but also displacement variations or phase changes. The vector at the output of the adaptive system has to be flipped to recover the normal forward direction. This recovered vector o1 can be written as a matrix o2 by using the

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vector-to-matrix conversion block (v2m), which performs the opposite operation than m2v. Finally, o2 can be used to obtain an “averaged” vector o3 by means of a maximum absolute value (MAV) operation. To avoid the influence of outliers, the samples of every column of o2 were sorted and the 5% on the top and the 5% on the bottom were trimmed out before applying the MAV. The MAV block selects, from every column of the matrix o2 after trimming, the sample whose absolute value is maximum to obtain the vector o3. 6.3.4 Adaptive enhancer evaluation

The adaptive enhancer of Figure 6.14 includes two main features that have to be tested. This scheme provides a matrix (output o2) including certain beat-to-beat information and, at the same time, yields an “averaged” vector (output o3) that can be used for an overall detection of the VLP, equivalent to the standard method. Beat-to-beat information

Figure 6.15 shows an example of how the adaptive enhancer + MSA recovers the HRECG signal from a noisy environment. The 60-heartbeat records shown in the figure were previously high pass filtered with a FIR filter of order 80 (Section 5.5.3) and windowed around the fiducial marks (-100ms/+156ms), to confine the 3-D plots. The time axis was reversed to see the VLP region (between 150ms and 200ms approximately). The plot on the top shows a clean Z-lead record with variable VLPs (cVLPj1). Observe, however, that no VLP can be recognized from the noise in the noisy signal nVLPj1 (central plot). The plot on the bottom represents the recovered signal by using the adaptive enhancer + MSA (output o2 in Figure 6.14). In the recovered signal, there is

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some distortion close to the steepest regions due to the adaptive algorithm.

This

distortion avoids following the exact VLP beat-to-beat structure, which is the main limitation of the adaptive scheme. However, the bottom plot in Figure 6.15 clearly shows the variable VLPs, which can be distinguished even in a beat-to-beat basis.

Figure 6.15 Example of the performance of the adaptive enhancer + MSA with a noisy variable-VLP record (Z-lead of nVLPj1).

As expected, the performance of the algorithm is better for lower levels of noise. It is important to note that, for the same level of noise, the algorithm performs better with non-VLP and fixed-VLP than with the variable-VLP records, although some distortion may be present close to the peaks. Figure 6.16 shows an example of that performance with a non-VLP noisy record (Z-lead of n1). Observe the contrast between the enhanced

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signals (those at the bottom) in the Figure 6.15 (variable-VLP) and Figure 6.16 (nonVLP).

Figure 6.16 Example of the performance of the adaptive enhancer + MSA with a noisy non-VLP record (Z-lead of n1).

A more detailed study, including 500 single heartbeats randomly chosen from the 1min test records of Section 4.5.5, showed that, although the enhancer performance was waveform dependent, the VLP detection was possible in a beat-to-beat basis. To be precise, more than 93% of the individual windowed heartbeats permitted a correct classification (CC>93%) of the records as VLP and non-VLP data after extracting the QRSd feature. It should be mentioned, however, that some records required manual

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adjustment of the onset and offset, which means that the standard way to find these points may not be compatible with the single heartbeat enhanced signal. Overall detection of VLP

The rationale for the MAV at the end of the enhancing scheme (Figure 6.14) was that the new MSA, used to generate the reference i for the adaptive enhancer, worked well in the isoelectric segments, providing good recovery of that part of the signal, but tended to attenuate the peaks. In the adaptation process, the higher instability is around those peaks because of the worse match between the main input i and the reference input r, and because of the adaptation process itself. The MAV block does not affect much the isoelectric segment, but it “catches” the peaks (including those in the VLP region) that are lost otherwise in the averaging process. In this case, the “averaged” vector o3 does not exhibit better noise reduction in the isoelectric segment than y, but a higher VLP-ISO difference, more evident in the presence of variable VLPs. Figure 6.17 shows the absolute value of the 60-heartbeat (Z-lead of nVLPj1) “averaged” signal by using the standard method (blue) and the adaptive enhancer + MAV, i.e. output o3 in Figure 6.14 (red), compared to the first heartbeat of the ideally clean signal cVLPj1 (black). It can be noticed that the standard averaging method works acceptably well in the isoelectric segments, but attenuates considerably the variable VLPs, making difficult to distinguish the offset of the QRS. However, the adaptive enhancing + MVA, although introduces some distortion, intensifies the differences between the isoelectric segment and the VLP region, making easier the recognition of the offset.

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180 Ideally clean (1st beat) Standard averaging Adaptive enhancer + MAV (o3 )

160

140

amplitude (uV)

120

100

80

60

40

20

0

50

100

150

200

250

time (ms)

Figure 6.17 Absolute value of the “averaged” signals compared to one ideally clean beat.

When the VLP are fixed (beat-to-beat repeatable), the distortion introduced by the algorithm can be discarded. For these cases, the offset is again easily distinguishable, providing a good discrimination between the VLP and the non-VLP subjects. A detailed study with the 1min test records, showed a perfect classification (CC=100%) for the enhancing + MVA scheme by using the QRSd as a discriminant feature. It should be mentioned that the automatic detection of the onset and offset failed in occasions in which the resultant isoelectric segment had some spikes due to adaptation problems. However, the manual correction was always effective to classify the records.

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6.4 2-D VLP detection scheme Traditional techniques for HRECG analysis are based on 1-D representations of the signal on the time domain, or 2-D representations containing t-f information. Here, a novel procedure (Figure 6.18) was designed to enhance and extract information from a 2D representation of the HRECG signal, which circumvents limitations of the signal “averaged” based schemes. The first part of this novel 2-D VLP detection scheme yields an N-by-256 (generally N ≤ 64) matrix x, in the same way used by the new adaptive enhancer with modified signal averaging (Section 6.3.3). This 2-D array x, containing approximately 64 windowed (256ms length) heartbeats, was considered as an intensity image. Consequently, imageprocessing techniques could be used for noise removal, edge detection and feature extraction to detect VLPs. 6.4.1 Noise removal from the 2-D HRECG signal

The image x typically includes noise that may mask the VLP information; therefore, a noise removal scheme has to be applied. Several linear, non-linear and adaptive filtering techniques [129] are available to remove noise from an image and could be used. However, in the scheme implemented here, a wavelet based denoising procedure was selected because of its properties (Section 3.6.4).

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HPF FIR M=80

s+n

windowing 1×l

ta’-lsa ~ ta’+rsa

ta ’

&

1×N

lead normalization

1×l

QRS detector lsa=100fs-1 rsa=156fs

N×(lsa+rsa+1)

2-D noise removal

x

2-D feature extraction

2-D edge detection

Detection/ Classification

Figure 6.18 2-D VLP detection scheme.

It is known that the denoising performance (Section 3.6.4) depends on several factors including the decomposition level, WP tree structure, wavelet family, thresholding scheme, and threshold level. These parameters can be estimated from the characteristics of the recorded HRECG signal by following different evaluation criteria. Because of the diversity of HRECG waveforms and contaminating noise in real clinical situations, there is not a universal set of parameters to accomplish an “optimum” wavelet packet denoising process. Therefore, a preliminary study compared the performance of several different schemes with multiple combinations of parameters.

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Levels of decomposition and tree structure

The windowing block of Figure 6.18 yields, by default, a 64-by-256 matrix, i.e. powers of 2 in both dimensions to ease the computational burden. This resulting image can be decomposed by up to 6 levels (26 = 64). However, the pre-processing high-pass filtering attenuates the lowest frequency components and, consequently, no relevant details are revealed after a certain level of decomposition. Several entropy-based criteria (Shannon, threshold, norm, log energy and SURE) were used to find the optimal decomposition level (Section 3.6.4). It was verified for a wide range of test signals that the level 3 was “optimal” for the decomposition of the 2-D HRECG signal. A visual evaluation of the decomposed signals coincided with the previous observation.

Therefore, the level 3 was taken as a default level of

decomposition for the denoising block of the 2-D VLP detection scheme. Given the flexibility provided by the WP, it is expected that the optimal tree is more likely to change depending on the input HRECG signal. The same entropy-based criteria corroborated this conjecture. However, it was found that the wavelet tree is a good compromise for most HRECG signals in the test set. Since a standard tree was needed to facilitate the denoising and further processing of the 2-D HRECG representations, the wavelet tree was deemed the best choice. Wavelet type and WT algorithm

Although several wavelet families (Section 3.6.5) provided comparable results, the quasisymmetric wavelet of order 4 (symlet 4) was selected for the 2-D detector scheme. This wavelet is nearly symmetric, avoiding excessive dephasing in the 2-D processing. It has

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compact support, with filters of length 8 (support width = 7), which allows for good time localization. In addition, its 4 vanishing moments for the mother wavelet is a good compromise to effectively attenuate the noise (long enough) without over-smoothing image details (not too long). To avoid the translation variance of the classical discrete wavelet transform (DWT), the stationary wavelet transform (SWT) algorithm was used. The SWT averages slightly different DWT (ε-decimated DWT) to obtained a representation that does not depend on the translation of the original signal. Consequently, the SWT decomposition structure is more tractable than that of the classical DWT. Thresholding and shrinking

A fixed threshold (level-dependent) method was found as a good predefined thresholding strategy for the 2-D detection scheme. However, as the HRECG may be corrupted by non-white noise, a level-dependent and orientation-dependent (horizontal, vertical and diagonal) thresholding method was chosen (Section 3.6.3). As expected, the vertical details of the decomposed image were those contributing the most to the reconstruction stage.

The horizontal details, however, were the least

dominant because of the high similarity of the consecutive heartbeats. This particular characteristic of the N-by-M HRECG image was taken into account to apply different weights influencing the universal fixed threshold before shrinking the horizontal, vertical and diagonal coefficients. The values of the universal threshold obtained for every level i were kept to shrink the coefficients of the diagonal details (γd), while diminished 50% for

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the vertical detail shrinking (γv) and increased 50% for the horizontal computations (γh). That is,

γ v = 0.5σ i 2 ln ( NM ) γ d = σ i 2 ln ( NM )

,

Eq. 6.10

γ h = 1.5σ i 2 ln( NM ) where σi is the standard deviation of the estimated noise in the i-th level. The shrinking stage used soft thresholding (Eq. 3.41), although results with hard thresholding were very similar. 6.4.2 Detection of onset and offset from the 2-D HRECG signal

After noise removal, the onset and offset of the 2-D QRS are estimated. Edge detection techniques, frequently used in image analysis, were used to detect such boundaries. The edges of interest here can be interpreted as the initial and the final curve, predominantly on the vertical direction, that follow a path of rapid change in the HRECG image “intensity” (amplitude), i.e. the transitions between the isoelectric segments (PQ and ST) and the QRS complex. To find the onset and offset in the HRECG image, a version of the Canny method [129] was preferred over the other edge detectors available because of its better performance in the presence of the remaining noise. This method finds edges by looking for local maxima of the gradient of the HRECG image, which was calculated using the derivative of a Gaussian filter with σ =1.

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To improve its immunity to noise, this version used two threshold levels estimated from the isoelectric area of the filtered HRECG image, a low threshold coinciding with three times the estimated standard deviation (3σiso) and a high threshold 2.5 times higher (7.5σiso). In this way, the algorithm detected strong and weak edges, and included the weak edges only if they were connected to strong edges. Two binary image masks were generated to assist in the next stage of feature extraction. The binary image onoff is a 64-by-256 matrix containing 1’s between the onset and the offset boundaries of the HRECG image and 0’s in all the other positions or “pixels”. The other image, vlp50, comprises 1’s between the offset line and a parallel line placed 50ms before, with 0’s everywhere else. To avoid problems close to the end of the 2-D arrays, the first 4 rows and the last 4 rows were forced to 0 in both binary masks. 6.4.3 Feature extraction from the 2-D HRECG signal

The classical time domain features, i.e. QRSd, LASd and RMS40, have been recognized as very good predictors to detect VLPs. Using these predictors provides less false positives and better reproducibility than using predictors from other methods [31] [209]. Therefore, 2-D versions of these features were extracted from the denoised HRECG to be used in the novel detection scheme. In addition to these time domain features, moment-based features (mean and variance) were obtained to characterize each sub-band image.

Concatenated moment-based

features that represent the original image, can be used in morphology classification of the HRECG. This constitutes a method of dimensionality reduction, as these few momentbased features replace the original 16 384 pixels.

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Feature equivalent to QRSd for the 2-D analysis

The duration of the filtered QRS (QRSd), measured from the onset to the offset, is the most relevant feature in the time domain analysis for the typical 1-D case. The area occupied by the filtered QRS complexes in the HRECG image is equivalent to the QRSd for the 1-D case. This new parameter (QRS) can be easily computed as the sum of the elements in the onoff mask. As the dimensions of the original HRECG image was fixed to 64-by-256 pixels, the highest values of the sum of the elements in onoff should be associated to the widest QRS complexes due to the presence of VLPs. Feature equivalent to RMS40 for the 2-D analysis

The RMS voltage from the offset to 40ms into the QRS (RMS40) measured from the 1-D filtered HRECG signal is another classical time domain feature. The equivalent measure for the 2-D HRECG representation (RMS) involves a region previous to the 2-D offset from which the variance is computed. After applying the FIR high pass filter of order 80, the QRS complex widens (Section 5.5.3) and consequently the region of interest (where the VLPs may appear) expands. Therefore, the area taken into account to compute the equivalent feature to the RMS40 was expanded to a width of 50ms. The matrix vlp50 obtained by the 2-D edge detection block was used as a mask to extract this region of interest. The parameter RMS is calculated as the root mean square value of the elements in this region. Lower values of this parameter are expected from VLP signals.

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Moment-based features for the 2-D analysis

Frequency domain features have also been used for VLP detection (Section 2.4.2). Since different combinations of low-pass and high-pass filters produce different sub-band images, they carry information of the frequency structure (morphology) of the original image. The mean and the variance can be computed from every sub-band image of the 3level decomposition (10) to provide morphology information of the 2-D HRECG. In this study, only the mean and the variance of the coefficients in the region of interest, from the 3 vertical details, were computed. This reduced the number of moment-based parameters to the 6 most relevant according to the typical structure of the HRECG image, which has higher variation in the vertical direction (time direction). However, for future studies on VLP classification, a higher number of moment-based features may be reasonable. To define the region of interest in the sub-band images (vertical details in this case), they were multiplied element-by-element by the mask vlp50. Then, the mean and the variance of all the elements of the masked vertical images were computed. 6.4.4 Detection/classification

The features extracted in the previous stage were used as predictors to classify the HRECG images in two groups: VLP records and non-VLP records.

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combinations of parameters with different subsets of data were studied by using best subset analysis, stepwise regression, linear regression, principal components and discriminant analysis (assisted by Minitab 13.31, www.minitab.com).

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The main goal of this work was to obtain a superior VLP detection than the traditional techniques. This was accomplished by using linear discriminant analysis on the extracted parameters. Although the way was paved, the classification problem was outside the scope of this work and it was not developed further.

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The first 64-heartbeat segment from every record of the set of test signals was used to evaluate the performance of the 2-D HRECG analysis scheme. Images of 64-by-256 pixels were developed from every individual lead record and the whole procedure applied.

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Figure 6.19 shows the approximation and detail (horizontal, vertical and diagonal) coefficients for 3 levels of decomposition of a typical HRECG image (ideally clean). The decomposition was performed by SWT with the symmlet4 wavelet. It can be seen that the 3 levels provide certain information on the signal, but the vertical details are the most prominent. The diagonal details suggest variability in the VLP region (between 140 and 190ms approximately), as certainly happened because of the simulation of variableVLP in the test signal cVLPj1 used for this example. The horizontal detail coefficients are the least significant of all. Figure 6.20, which shows similar decomposition of a noisy signal, confirms this trend.

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Based on that pattern, the coefficients were shrunk by using position-dependent thresholding (Eq. 6.12). Figure 6.21 shows the decomposition of the resulting denoised HRECG image. Observe that the details now give better idea of the HRECG structure.

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In general, the wavelet-denoising scheme here used provides very enhanced images that facilitate the edge detection process.

Figure 6.22 shows HRECG images before and

after denoising for the two extreme cases, ideally clean signals (cVLPj1) and severely contaminated images (nVLPj1). It can be distinguished that, opposite to other noise removal methods, the ideally clean signal did not suffer any important blurring or distortion after applying the SWT denoising tool.

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HRECG representation was significantly improved, revealing the VLP structure masked by the noise in the original image. It should be mentioned that no ringing was produced after denoising the non-VLP images. Consequently, the denoised HRECG image always resembles the original ideally clean representation and it is suitable for VLP detection.

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The SWT denoising scheme yields an acceptably clean image, but certain interference may persist. Therefore, the masks used for feature extraction, onoff and vlp50, were obtained by an algorithm based on the Canny edge detection method which is less likely to be confused by noise. Such algorithm achieved very good performance with the denoised images.

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Figure 6.23 illustrates, with an example, the considerable repeatability of the mask generation.

The white regions in the masks represent the areas from the denoised

HRECG image or the detail coefficient sub-band images that should be taken into account for the feature extraction (Section 6.4.3). It can be perceived from this example that the edge detection based algorithm can track the borders of the QRS complex (onset and offset) from clean images and from denoised noisy images in a very similar way.

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The repeatability on the mask generation leads to consistent feature extraction (Section 6.4.3). From every individual lead, the parameters equivalent to the QRSd and RMS40 (QRS and RMS respectively), and the mean and variance of the 3-level vertical detail

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coefficients (mean1~3 and var1~3) were estimated. The image associated to the vector magnitude V and its “decomposition” sub-images were obtained as the RMS sum of the denoised individual leads. All these extracted features were included in Appendix J. By using all the 32 extracted features (8 per lead) as predictors at the same time, a perfect classification was achieved (CC = 100%) by linear discriminant analysis with cross validation. The squared distance (Mahalanobis distance) between groups was as high as 92.52, allowing this remarkable result. However the number of extracted features or predictors can be considered excessive. Stepwise (forward and backward) regression and best subsets regression were performed to identify the best fitting regression models that can be constructed with the predictor variables. All possible subsets of the predictors were evaluated and the two best models that can be constructed for each number of predictors were reported. Models using less than 12 predictors at a time, although produced high R2 (coefficient of determination) and adjusted R2 parameters, yield Mallow’s Cp statistics much higher than the number of parameters in the model. Therefore, more than 12 parameters should be used to obtain an excellent classification. The adjusted R2 value reached values up to 94.7% and the square root of the MSE of the model (s) was as low as 0.11. Similar analysis was performed with the subsets of predictors corresponding to the individual leads (maximum of 8 predictors at a time). The results were lead dependent, with the X-lead providing the best results and the Z-lead giving the worst classification, which coincided with Waldo’s observations in [212]. To be more precise, predictors associated with the Z-lead gave an adjusted R2 of 63.7% for the best case, while

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predictors related with the X-lead gave values of adjusted R2 up to 82.6% with Cp close to the number of parameters in the model. However, even better results were suggested with the predictors linked to the equivalent vector magnitude V, which yield adjusted R2 values higher than 85%, with s lower than 0.2. This result makes sense, since the set of predictors associated to V contained information from all the individual leads. The predictors more likely to be included in the best models suggested by the best subsets regression for the individual lead analysis were QRS and RMS. However, the mean and the variance computed from the vertical detail coefficients of the third decomposition level (mean3 and var3) were the most important parameters for the models derived from the composite vector V. A very good compromise, for instance, was obtained with the predictors RMS, mean2, mean3 and var3 connected to V.

Predictor Constant RMS mean2 mean3 var3

Coefficients SE coeff. T value 1.14910 0.04170 27.55 0.00004192 0.00001362 3.08 0.048465 0.005432 8.92 -0.040587 0.001947 -20.85 0.00002369 0.00000287 8.27 Table 6.2 Linear regression analysis results.

p value 0.000 0.002 0.000 0.000 0.000

Table 6.2 reviews the results of linear regression analysis performed with this subset of predictors (RMS, mean2, mean3 and var3). The regression equation that describes the relationship between the response (type) and the predictor variables was, type = 1.15 + 0.000042RMS + 0.0485mean2 – 0.0406mean3 + 0.000024var3 . Eq. 6.11 The standard error for all the estimated coefficients (SE coeff.) was very small. In addition, it was found that all the predictors were statistically significant, with p values considerably smaller than the level of significance (α = 0.05). 224


Linear discriminant analysis using cross-validation achieved a 97.5% of correct classification (CC) with these four predictors. Only 5 out of 136 VLP subjects were incorrectly classified as non-VLP (5 FP), but all the 68 non-VLP subjects were correctly classified (0 FN). This means that the specificity was increased to 93.2% and the positive predictive value up to 96.3%, while the sensitivity and negative predictive value were 100%. A squared distance between groups of 26.03 supported this successful VLP detection.

6.5 Conclusions Combining enhanced traditional techniques with very novel procedures, especially designed here, offers great flexibility to detect and analyse VLPs. The VLP processing schemes here implemented, considerably improved the VLP detection.

The traditional time domain analysis was improved by the use of a better QRS detector (Section 5.4) and an FIR high pass filter (Section 5.5). However, the main contribution to this time domain analysis was the introduction of the modified signal averaging MSA, which is an extension of the modified trimmed mean filter [157] and achieved a good compromise between mean and median filters. The MSA proved to be robust in the presence of outliers. It achieves acceptable edge preservation, based on the rejection of the displaced samples that differs the most from the median of every original column. The most remarkable feature of the MSA is its excellent noise attenuation within the isoelectric segments, which outperformed the typical coherent averaging and allows reducing, to less than 60, the number of heartbeats to be processed.

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When running in full automatic mode, both methods, the coherent averaging based and the one with MSA, had certain limitations to find the onset and offset of the filtered QRS. Therefore, the features extracted (QRSd, LASd and RMS40) were affected in occasions, and the sensitivity and specificity were consequently low (~70% and 80% respectively), with a slightly better performance of the MSA-based procedure.

The manual adjustment of the QRS endings, which is easily to be performed with the PCbased system, consistently improved the VLP detection. The MSA, which provided better noise reduction within the isoelectric segments, allowed a more precise adjustment, and better VLP detection as a result.

The new adaptive enhancer designed here performs the filtering of the windowed heartbeats (in the backwards direction) by means of an RLS algorithm, with 2 weights and forgetting factor of 0.95. A quality reference was obtained by MSA of the original signal. This scheme allows extracting certain beat-to-beat information from the HRECG signal. A limitation of this technique is that it cannot follow every single change in a beat-to-beat basis.

However, a combination of this enhancer with a maximum absolute value (MAV) operation achieved excellent VLP detection, although some manual adjustments may be needed.

A final novel scheme for VLP detection was based on the 2-D representation of the HRECG. In this case, the HRECG image was denoised by 3-level SWT with level dependent and orientation dependent thresholding. This noise removal technique did not

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introduce appreciable distortion, while attenuating considerably the background noise. The detection of the onset and offset was performed with an edge detection algorithm based on the Canny method.

The immunity to noise of this algorithm allows a

consistently precise detection of the borders of the filtered QRS, and therefore a good feature extraction.

The features extracted from the filtered (denoised) HRECG image were based on the typical features used for the time domain analysis and certain moment-based features (mean and variance of the detail coefficients at different levels of decomposition). Combinations of both kinds of features provided excellent VLP detection. Detection based on features associated to the composite image representation V outperformed those based on the individual leads. In general, the 2-D analysis of the HRECG obtained much better results than the equivalent traditional 1-D analysis.

These techniques, introduced here by the first time, represent a prominent step forward in the VLP detection/classification problem. However, new assessments with real world records are needed before using them in a clinical environment.

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Chapter 7 - Conclusions.

Chapter 7 - Conclusions To conclude this work, the main contents of the thesis are summarised, paying particular attention to the accomplishment of the objectives. Then, the principal contributions of this work are stated. Finally, a number of interesting topics are proposed for future investigation based on the findings and limitations of this work.

7.1 Summary Introduction VLPs are low-amplitude, broad-band-frequency waveforms in the HRECG associated with certain life-threatening cardiac diseases. Consequently, the detection of VLPs can be used as a non-invasive diagnostic marker. However, their detection constitutes a challenge because VLPs are masked by the other components of the ECG and noise and interference, both in time and frequency domains. The detection and analysis of the HRECG records require special acquisition systems, and digital signal processing algorithms for the SNR enhancement and analysis of the signal of interest, i.e. VLPs. The basic guidelines for the acquisition stage [26] recommend the use of Ag/AgCl electrodes placed as in the XYZ lead system. Every channel requires a CMRR higher than 120dB [33] and a minimum bandwidth between 0.5 and 250Hz. In addition, the differential gain and the characteristics of the A/D converter should guarantee a resolution better than 2.5µV. To complete the requirements, the sampling frequency should not be less than 1kHz.

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The most commonly used noise reduction strategy for VLP detection is the coherent averaging, which assumes additive random noise and a perfect alignment between the signals of interest in every heartbeat.

This averaging process needs around 300

heartbeats and may introduce a severe low pass filtering effect due to misalignments, not to mention that the beat-to-beat information is completely lost. To overcome these limitations, different alternative approaches have been taken, including optimal filtering, adaptive filtering, high order statistics and denoising with wavelets. The analysis of the enhanced signal can be conducted in the time or in the frequency domains. The time-domain analysis employs a high-pass filtering to enhance the VLPs, while attenuating the other components of the ECG and the noise and interference. To avoid ringing and to ensure that the onset and offset of the filtered QRS coincide with those in the original signal, Simson [182] proposed a bi-directional four-pole Butterworth high-pass recursive digital filtering, which was, later, adopted as standard [26]. This filter, however, cannot be applied in a single direction.

In addition, it introduces

distortion within the QRS complex due to its non-linear phase characteristic. The time-domain analysis is completed by extracting the features QRSd, LASd and RMS40 and comparing them with pre-established threshold values [26]. This analysis provides less false positives than other methods and it has the best reproducibility [31] [209]. Nevertheless, the noise level and the number of averaged heartbeats affect timedomain analysis and high-pass filters may introduce artificial signals, which affect the final results.

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On the other hand, frequency-domain analysis schemes do not need high-pass filtering and, unlike the time-domain implementation, can be applied to patients with bundle branch block. However, these techniques depend on window functions that introduce pseudo peaks due to finite data length [145], and the results have a high variability [209]. Given the highly non-stationary nature of the HRECG, this approach is not suitable for VLP analysis [122]. In recent years, great attention has been focused on the time-frequency (t-f) and the timescale (WT and WP) representations.

These multidimensional representations have

certain appealing for VLP analysis, providing more information [107] and solving some of the limitations of the independent time- and frequency-domain analyses. WT has been claimed as the best t-f choice for HRECG signal analysis [124] [61]. However, the main problem of the t-f analysis for VLP studies is its lack of simultaneous resolution in time and frequency axes [126]. In addition, distinction between normal and abnormal signal components is very difficult because of the low t-f energy concentration [122], and, consequently, the reproducibility of these tests is very poor [209]. Therefore, t-f analysis is not reliable for clinical applications in its present state. Objectives The main objective of this investigation was to improve VLP detection, by designing algorithms that could be used in computer-based HRECG analysers and overcome limitations of the current techniques. To be precise, it was expected: •

To reduce the number of heartbeats required, diminishing the acquisition and processing time.

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To be more robust with non-stationary data.

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To enable to obtain specific beat-to-beat variability information.

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To provide the means to extend the analysis to the whole QRS complex.

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To increase the sensitivity and specificity in the VLP detection.

Materials and methods To evaluate the new algorithms developed in this thesis, a HRECG database, including XYZ 5min records from approximately 60 post-MI patients and 60 healthy volunteers, was created. For the data collection, it was utilised an affordable PC-based system with 4 channels, the fourth of which was used for a common mode signal Vcm. Every channel included a low-noise pre-amplifier, an isolation amplifier, and low-pass and high-pass filters [207]. The use of a 16bit A/D converter and a differential gain Ad=800 guaranteed a resolution better than 0.19µV. In addition, the bandwidth was set to Bw=0.5-300Hz, and the sampling frequency to fs=1kHz. All the processing algorithms were implemented as GUIs in MATLAB 5.3 (fully compatible with MATLAB6.0, release R12) to provide flexibility.

After analysing the characteristics of the real data, simulations of the HRECG signal, VLP and noise were also designed.

The combination of synthesised and semi-

synthesised waveforms provided a realistic and, at the same time, controllable environment for algorithm assessment.

The basic clean heartbeats were extracted from real HRECG data (clean non-VLP signals). Random-generated sequences resembling the characteristics of the VLPs were

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added to the clean non-VLP records. The position of these basic VLP waveforms was fixed (fixed-VLP records) or randomly varying (variable-VLP records). Every clean record, non-VLP, fixed-VLP and variable-VLP, was contaminated with typical ECG noise to obtain the noisy non-VLP, noisy fixed-VLP and noisy variable-VLP records, respectively.

The algorithms here designed and evaluated comprised pre-processing and processing schemes. The most important pre-processing design was a novel powerline interference canceller, based on an isoelectric interval detector, which does not introduce ringing effects.

A QRS detector and FIR high-pass filter designs also achieved significant

improvements. These designs although used in this work for HRECG analysis, have applications on other areas of cardiology.

On the other hand, the VLP processing techniques included an enhanced time domain analysis based on a new modified signal-averaging (MSA) scheme. As an evolution, a novel adaptive enhancer with MSA and maximum absolute value (MAV) “averaging” was designed to obtain certain beat-to-beat information and to emphasise the onset and offset of the QRS complex. Finally, a revolutionary 2-D VLP detection scheme was implemented, including SWT denoising, Canny edge detection, and moment-based feature extraction.

Results and discussion The new powerline interference canceller was based on a first order RLS adaptive algorithm, with forgetting factor of 0.99 to manage certain changes in the characteristics

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of the interference, using the signal Vcm as a reference. This canceller, however, stops adaptation during the non-isoelectric segments to avoid the ringing effect.

Unlikely the traditional interference cancellers, the new algorithm proved to considerably attenuate the interference components, while preserving the signal of interest without appreciable distortion. For instance, a powerline interference with variance of 201.62µV2 and bias of 13.1µV can be reduce to a variance of 24.5µV2 and bias of 3.9µV, while the time domain analysis parameters are kept compared with the clean signal.

It should be mentioned that an automatic isoelectric interval detector was used to implement the new canceller. However, this detector can be used as well to characterise the noise in the HRECG data and to implement other signal enhancement and analysis algorithms. The QRS detector implemented here is an enhanced version of the double-level algorithm [106] (EDL), with an optional cross-correlation adjustment (CCA) to refine the fiducial marks. The PC-based system allows the user to select the reference channel from the individual leads X, Y, Z (positive or negative peaks), and a new composite signal here proposed. The use of the new composite channel yielded, as an average, better results than the individual leads X, Y, and Z. A detailed evaluation with a novel procedure showed that the trigger jitter associated with these algorithms is normally < 0.5ms. A new FIR high-pass filter design based on a combination of an all-pass and a binomial low-pass filter was also introduced. This filter, with an order of 80, was confirmed to be a good compromise for high noise attenuation and low widening of the QRS complex,

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outperforming other FIR designs reported in the VLP literature. Therefore, it constitutes a good alternative to the Simson technique that can be applied in a single direction without signal distortion. The time-domain analysis improved robustness and repeatability by using a new modified signal-averaging (MSA) scheme. This is a combination of mean and median filtering. The enhanced technique easily rejects outliers and may reduce significantly the number of heartbeats (3, 5 or more times) to achieve a particular SNR. However, the standard method to automatically find the onset and offset of the filtered QRS may fail with this scheme. Another processing technique designed here was an improvement to the ALE plus MSA signal enhancement described in [202]. This set-up used the new MSA to obtain a good quality reference for an RLS adaptive enhancer, with order one and forgetting factor of 0.95 to accommodate to the non-stationary HRECG signal.

The filtering of the

windowed heartbeats was in the backward direction to avoid ringing in the VLP region. This scheme allows extracting certain beat-to-beat information from the HRECG signal, although it cannot follow every single change.

In addition, a combination of this

enhancer with a maximum absolute value (MAV) operation achieved excellent VLP detection, when helped by some manual adjustments.

Finally, a novel technique enhanced and extracted information from the 64-by-256-pixel HRECG image built with less than 64 windowed heartbeats (length of 256ms). The 2-D array was denoised with shift-invariant SWT and thresholding adapted to the decomposition level (assumes non-white Gaussian noise) and to the orientation (vertical,

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diagonal and horizontal), providing remarkable results.

The Canny edge detection

method was adjusted to generate masks that cover the whole QRS complex region and the last portion of it. These masks were used to extract 2-D features equivalent to those in the traditional time-domain analysis, along with moment-based features that provide excellent classification of VLP and non-VLP patients.

In the test stage, values of

sensitivity and specificity of 100% were obtained with certain combinations of features, excelling any other previous evaluated technique. Conclusions The number of heartbeats needed for the processing algorithms here designed was decreased to less than 60 (i.e. approximately 5 times less than for the standards.) By reducing the acquisition time, the HRECG signal is less likely to exhibit non-stationary behaviour; nevertheless, the algorithms implemented here have a limited capability to handle non-stationarities in the data (forgetting factors < 1, MSA which rejects outliers, wavelet thresholding depending on decomposition levels, Canny method to detect edges, etc.). Both the new adaptive enhancer plus MSA and the 2-D detection scheme, provide beatto-beat information. These methods, helped by the FIR filter design, provide the means to extend the analysis to the whole QRS complex, although simulations and tests here were focused on the last portion of the QRS complex and initial part of the ST segment. Although some other tests have to be performed before definitively introducing these algorithms to the clinic application, the results so far show a great improvement in the sensitivity and specificity. All the processing techniques assessed, outperformed the

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classical time-domain analysis method. The best results were obtained with the new 2-D VLP detector, which achieved perfect classification (SE=100% and SP=100%) in full automatic fashion by using certain combinations of features. All the objectives of this research were fulfilled.

Improved pre-processing and

processing algorithms to detect and analyse VLPs allow for better diagnosis capabilities. Therefore, the results of this work will have a direct impact on the lives of many individuals.

7.2 Original Contributions The main original contributions of this work to the VLP analysis are summarised as: 1. The creation of a HRECG database (Chapter 4) with a large variety of waveforms that allows evaluating not only HRECG-focused algorithms but also more general ECG schemes. 2. An automatic isoelectric interval detector (Section 5.2) that isolates only-noise sequences from the HRECG records and can be used to characterise the contaminating noise, or as part of certain SNR enhancing schemes. 3. A novel powerline interference canceller (Section 5.3), which outperforms traditional cancellers without appreciable distortion of the ECG signal. 4. A robust QRS detector (Section 5.4) that combines the enhanced double-level (EDL) algorithm with the cross-correlation fine adjustment (CCA). In addition, the way to objectively evaluate these QRS detector algorithms constitutes a contribution itself

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because it can be applied with any real multi-lead system records, without needing any other information. 5. A new FIR high-pass filter design (Section 5.5) based on a combination of an all-pass and a binomial low-pass filter. 6. A modified signal averaging MSA (Section 6.2.3), which is a custom modification to the modified trimmed mean filter [157]. This allowed a significant reduction of the number of heartbeats, rejected outliers and achieved acceptable edge preservation. 7. A new adaptive enhancer plus MSA (Section 6.3.3) that can extract certain beat-tobeat information.

In addition, a combination of the enhancer with a maximum

absolute value (MAV) operation achieved excellent VLP detection. 8. A 2-D VLP detection scheme (Section 6.4) and its components: •

Building the HRECG image by windowing approximately 60 heartbeats and completing a 64-by-256-pixel array (periodic image extension on both directions horizontally).

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Noise removal by shift-invariant SWT denoising, with level-dependent and orientation-dependent thresholding.

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Detection of onset and offset by means of a modified Canny edge detection algorithm.

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Feature extraction, including time-domain-like and moment-dependent features.

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7.3 Limitations of this work and directions of future research Several interesting topics on VLP were not covered thoroughly because of the limited time frame of this thesis. This compilation, however, can be the basis for future research. A few examples of the limitations of this work are listed along with directions for future investigation: 1. New real HRECG data have to be used to evaluate the algorithms designed here before using them in a complete clinical application. Different databases collected by other researchers, if available, can be used for this purpose.

In addition, some

suggestions can be given to improve the extension of the current HRECG database: •

The sampling frequency should be set at 2kHz to provide a better rejection of aliasing components and better accuracy of the QRS detector. This will tend to double the data size, but as the length of the records can be limited to 1min, instead of 5min, it will not affect much.

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The background noise should be minimised. Reducing the acquisition time to 1 min eases the patient cooperation and reduces chances of non-stationary data. A better skin preparation is expected as well as the use of certain shielded room if possible.

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More detailed information from patients would be useful for the final assessment of the algorithms. This should include a detailed follow-up during a 2-year period, with multiple records from the same subject and results of complementary tests (EPS, HRV, LVEF, etc.).

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2. Although the manual adjustment of the onset and offset of the QRS, available in the current PC-based HRECG analyser, consistently improved the VLP detection results compared to the typical automatic detector (Section 6.2.7), it may carry subjectivity. Therefore, an automatic onset-offset detector compatible with the MSA should be designed and tested to improve the full automatic detection of the VLPs with the enhanced time-domain analysis scheme and the adaptive enhancer plus MSA. 3. Using the equivalence between the adaptive enhancer filter weights after convergence and AR model parameters (Section 3.4.1), the spectro-temporal characteristics of the HRECG signal can be computed. This t-f representation may help in the VLP detection, after segmenting conveniently the weight parameter matrix to isolate the region of interest. 4. After an initial classification of the HRECG records into VLP and non-VLP records (VLP detection), a second stage to classify VLP records into different classes could be attempted to refine the diagnostic even more. This further classification could be achieved by using the moment-based features that carry certain morphology information; in a similar way than the texture classification is performed. The use of artificial neural networks could help to complete this idea. 5. All the simulations and tests performed here were focused to the VLP detection problem. However, some of the tools developed can be easily extended to analyse the abnormal intra-QRS waveforms. The 2-D VLP detection scheme, for instance, shows great potential for this purpose.

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6. Finally, the best performing algorithms assessed here and in future work should be integrated in a more general risk stratification system, which should include HRV and some other tests.

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[204] N. V. Thakor and D. Sherman, “Wavelet (Time-Scale) Analysis in Biomedical Signal Processing,” in The Biomedical Engineering Handbook, J. D. Bronzino, Ed. Boca Raton: CRC Press: IEEE Press, 1995, pp. 886-906. [205] K. Tamura, H. Tsuji, T. Nishiue, S. Tokunaga, and T. Iwasaka, “Association of preceding angina with in-hospital life-threatening ventricular tachyarrhythmias and late potentials in patients with a first acute myocardial infarction,” Am. Heart J., Vol. 133, No. 3, pp. 297-301, 1997. [206] N. V. Thakor and Y-S. Zhu, “Applications of Adaptive Filtering to ECG Analysis: Noise Cancellation and Arrhythmia Detection,” IEEE Trans. Biomed. Eng., Vol. 38, No. 8, pp. 785-793, 1991. [207] 8-Channel Signal Acquisition System CIDA/UNB/UCLV. Users Manual, UNB, Fredericton, 2000. [208] R. Vázquez, E. B. Caref, F. Torres, M. Reina, J. A. Guerrero, and N. El-Sherif, “Reproducibility of time-domain and three different frequency-domain techniques for the analysis of the signal-averaged electrocardiogram,” J. Electrocardiol., Vol. 33, No. 2, pp. 99-105, 2000. [209] R. Vázquez, E. B. Caref, F. Torres, M. Reina, J. Huet, J. A. Guerrero, and N. El-Sherif, “Comparison of the New Acceleration Spectrum Analysis with Other Time-and Frequency-Domain Analyses of the Signal-Averaged Electrocardiogram,” Eur. Heart J., Vol. 19, No. 4, pp.628-637, 1998. [210] A. Voss, J. Kurths, and H. Fiehring, “Frequency Domain Analysis of Highly Amplified ECG on the Basis of Maximum Entropy Spectral Estimation,” Med. Biol. Eng. Comput., Vol. 30, No. 3, pp. 277282, 1992. [211] L. La Vecchia, R. Ometto, F. Bedogni, G. Finocchi, G. M. Mosele, L. Bozzola, P. Bevilacqua, and M. Vincenzi, “Ventricular late potentials, interstitial fibrosis, and right ventricular function in patients with ventricular tachycardia and normal left ventricular function,” Am. J. Cardiol., Vol. 81, No. 6, pp. 790-792, 1998. [212] D. J. Waldo, P. R. Chitrapu, B. R. S. Reddy, K. Jepsen, G. A. Kidwell, and A. J. Greenspon, “Use of Wigner-Ville distribution to analyze cardiac late potentials,” in Proc. IEEE/12th Ann. Conf. Eng. Med. Biol. Soc., pp. 825-826, 1990. [213] X. Wang, S. Kamakura, K. Matsuo, M. Ogawa, Y. Tanabe, and K. Shimomura, “Relation between spatial distribution of late potentials and location of origin of premature ventricular complexes on body surface map in patients with postinfarction ventricular tachycardia,” Int. J. Cardiol., Vol. 72, No. 2, pp. 111-119, 2000. [214] S. Wu, Y. Qian, Z. Gao, and J. Lin, “A novel method for beat-to-beat detection of Ventricular Late Potentials,” IEEE Trans. Biomed. Eng., Vol. 48, No.8, pp. 931-935, 2001. [215] X.-G. Xia and V. C. Chen, “A Quantitative SNR Analysis for the Pseudo Wigner-Ville Distribution,” IEEE Trans. Signal Processing, Vol. 47, No. 10, pp. 2891-2894, 1999. [216] Q. Xue and B. R. S. Reddy, “Late Potential Recognition by Artificial Neural Networks,” IEEE Trans. Biomed. Eng., Vol. 44, No. 2, pp. 132-143, 1997. [217] Y. Xu, J. B. Weaver, D. M. Healy Jr., and J. Lu, “Wavelet Transform Domain Filters: A Spatially Selective Noise Filtration Technique,” IEEE Trans. Image Processing, Vol. 3, No. 6, pp. 747-758, 1994. [218] J. Zhang and Z. Bao, “Initialization of Orthogonal Discrete Wavelet Transforms,” IEEE Trans. Signal Processing, Vol. 48, No. 5, pp. 1474-1477, 2000. [219] X. P. Zhang and M. D. Desai, “Adaptive Denoising Based on SURE Risk,” IEEE Signal Proc. Letters, Vol. 5, No. 10, pp. 265-267, 1998. [220] D. P. Zipes, J. P. DiMarco, P. C. Gillette, W. M. Jackman, R. J. Myerburg, and S. H. Rahimtoola, “Guidelines for Clinical Intracardiac Electrophysiological and Catheter Ablation Procedures,” J. Am. Coll. Cardiol., Vol. 26, No. 2, pp. 555-573, 1995. (Also available at http://www.acc.org/clinical/guidelines/ablation/73522.pdf)

253

Appendix A: Consent Form

CONSENT FORM Improving Ventricular Late Potential Detection Effectiveness Principal investigator: MSc. Alberto Taboada Crispí, Ph.D. Candidate. University of New Brunswick, Biomedical Engineering. Purpose of the work: The objective of this study is to improve Ventricular Late Potential (VLP) detection/estimation as a non-invasive diagnostic marker for sustained ventricular tachycardia (sVT) and sudden cardiac death (SCD). Methods: VLPs are low amplitude signals, found in the High Resolution Electrocardiogram (HRECG) of patients prone to sVT and SCD, after myocardial infarction (MI). New algorithms are being developed to overcome limitations of the current techniques for signal enhancing and VLP detection/estimation. Before being used in a clinical environment, signal-processing algorithms have to be evaluated by using real HRECG signals from post MI patients and healthy volunteers with no evidence of heart abnormalities as a control group. To acquire the HRECG signals, seven disposable electrodes (Red DotTM) have to be placed on the subject’s skin (see figure). Before this, the skin surface should be cleansed thoroughly with alcohol and abraded to assure a good reduction of noise and interference.

Risk: Equipment used in this acquisition process fulfils international safety standards for medical equipment (IEC 6101). This is a non-invasive procedure, similar to conventional electrocardiography, with almost no risk in normal conditions. Subjects might feel a slight discomfort during the skin preparation or electrode removing. Consent: I, _____________________________________________________, hereby consent to participate as a subject in this research project. I acknowledge that the researcher has explained the purpose and procedures of the study, and that any clarifications I have requested have been answered to my satisfaction. I understand that I am free to withdraw consent and discontinue participation in the study without prejudice at any time. By signing this consent I am also assured that the data and the information obtained in this study will be used only for the purpose stated above, and that my identity as a subject will remain confidential. Subject: Witness: Date:

. Signature: . Signature: . 254

Appendix A: Consent Form

INFORME DE COMPROMISO Mejora de la efectividad en la detección de Potenciales Tardíos Ventriculares Investigador Principal: MSc. Alberto Taboada Crispí. Propósito del trabajo: El objetivo de este estudio es mejorar la detección/estimación de los Potenciales Tardíos Ventriculares (VLP) como un marcador diagnóstico no invasivo para la taquicardia ventricular sostenida (sVT) y la muerte súbita cardiaca (SCD). Métodos: Los VLPs son señales de baja amplitud, encontradas en el Electrocardiograma de Alta Resolución (HRECG) de pacientes propensos a sVT y SCD, después de un Infarto al Miocardio (MI). Nuevos algoritmos están siendo desarrollados para superar las limitaciones de las técnicas actuales para el mejoramiento de la señal y de la detección/estimación de los VLPs. Antes de usarlos en un ambiente clínico, los algoritmos tienen que ser evaluados usando señales HRECG reales de pacientes postinfartados y de voluntarios sanos sin evidencias de daño cardíaco como grupo de control. Para adquirir las señales HRECG, siete electrodos desechables (Red DotTM) tienen que ser colocados sobre la piel del paciente (ver figura). Previamente, la superficie de la piel tiene que ser limpiada completamente con alcohol y lijada para asegurar una buena reducción de ruidos e interferencias.

Riesgo: El equipo usado en este proceso adquisición cumple las normas internacionales de seguridad para equipos médicos (IEC 6101). Este es un procedimiento no invasivo, similar a la electrocardiografía convencional, con casi ningún riesgo en condiciones normales. Los sujetos pudieran sentir una ligera molestia durante la preparación de la piel o al retirar los electrodos. Consentimiento: Yo, __________________________________________, por este medio expreso mi consentimiento para participar como sujeto en este proyecto de investigación. Reconozco que el investigador me ha explicado el propósito y procedimientos del estudio, y que todas las aclaraciones que he solicitado han sido respondidas a mi gusto. Entiendo que soy libre de retirar mi consentimiento y abandonar el estudio en cualquier momento sin daños o perjuicios. Firmando este consentimiento también aseguro que los datos y la información obtenidos serán usados solo para el propósito establecido anteriormente, y que mi identidad como sujeto permanecerá confidencial. Sujeto: Testigo: Fecha:

. . .

255

Firma: Firma:

Appendix B. Patients

ID p01 p02 p03 p03b p04 p05 p06 p07 p08 p08b p09 p09b p10 p10b p11 p12 p13 p14 p15 p15b p16 p17 p18 p18b p19 p20 p21 p22 p22b p23 p24 p25 p26 p27 p28 p29 p30 p31 p32 p33 p34 p35 p36 p37 p38 p38b p39 p40 p41 p42

W 1 1

race B

1 1 1 1 1

A

sex M F 1 1 1

60 173

89 54 58 67

65 60 55 62

160 25.4 166 21.8 166 20 160 24.2

1 1

1 1 1

1

32

90 181 27.5

1

1

1

58

70 168 24.8

83

55 160 21.5 90 55 90 59

31.9 20.2 27.8 21.2

1 1

1 1 1

1

Wall hgt BMI thr block cm Ant. Lat. Inf. Post. Sept. 169 29.8 1 1 1 170 21.8 1 1 1

59

1

1

wgt kg 42 85 63 63

ag.

1

1

1 1 1 1

1 1 1

60 62 34 54

1

1

60

90 168 31.9

1 1

1 1

74 54

1

1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1

1 1 1

1

-

1

-

1

1

-

84 172 28.4 53 160 20.7

1 1

1

-

55

74 165 27.2

1

1 1

46 45 72

78 160 30.5 75 170 26 70 170 24.2

1

60

70 160 27.3

1

1

1

1

1 1 1 1 1 1 1 1 1 1 1

83 50 156 20.5 56 96 167 34.4 76 70 170 24.2 66 60 158 24 66 75 170 26 61 75 173 25.1 55 70 170 24.2 58 56 158 22.4 42 105 180 32.4 75 45 150 20 63 90 180 27.8 54 53 160 20.7 74 45 150 20 76 60 170 20.8 41 77 198 19.6

1

1

59

56 171 19.2

1

1 1 1 1

1 1 1 1

74 71 57 40

70 57 66 70

1 1 1

182 21.1 170 19.7 166 24 155 29.1

256

1

1 1

1

1

1

1

168 165 180 167

20

1 1

1 1 -

1

1 1 1 1 1 1

1

1 1

1 1 1 1 1 1

1 1

1 1

1 1

1 1

1 1

1 1 1 1 1 1 1

1

1

1 1

1

1 1 1 1 1

1


ID

W 1 1 1

race B

A

p43 p44 p45 p46 1 p46b p48 1 p49 1 p50 1 p50b p51 1 p52 1 p53 1 p54 1 p54b p55 1 p56 1 p57 1 p57b p58 1 p59 1 p60 1 p60b p61 1 p62 1 m,C 57 3 1 std,% 93.4 4.9 1.6

sex M F 1 1 1 1

wgt kg 52 80 62 81 55 55

ag.

Wall hgt BMI thr block cm Ant. Lat. Inf. Post. Sept. 160 31.3 1 1 180 25 1 1 165 20.2 1 -

60

90 169 31.5

59 47

55 169 19.3 72 170 24.9

1

77

76 161 29.3

1

70 170 24.2 90 168 31.9 61 168 21.6

1 1 1

1

1

65 73 57

1 -

1

57

78 166 28.3

1

1

-

1 1

64 36

88 158 35.3 76 167 27.3

1

66

70 170 24.2

1

1

1

1 1

38 51

75 180 23.1 74 170 25.6

1

1 1

-

1

77

63 163 23.7

1

1 1 51 84

47 47 59 13

74 170 25.6 1 63 163 23.7 1 70 168 25 27 4 23 7 13 8.2 4.2 36.5 5.41 31.1 9.46

1 1

1 1

10 16

257

1

1

1

1 1 -

1

1

1

1 1

1

1

17 23

1 1 31 53

1 12 20.3


ID p01 p02 p03 p03b p04 p05 p06 p07 p08 p08b p09 p09b p10 p10b p11 p12 p13 p14 p15 p15b p16 p17 p18 p18b p19 p20 p21 p22 p22b p23 p24 p25 p26 p27 p28 p29 p30 p31 p32 p33 p34 p35 p36 p37 p38 p38b p39 p40 p41 p42

day MI days HBP diab ang 1

multi PVC Other comments MI 1 Lost original record. 1 X leads off!

1 6

acute acute

2

acute

2 2 3 3

acute acute acute acute

4

acute

1

1

acute

1

2

acute

1

2 2 1 2


1 1

1

1

1

17

healing

2 3 0 7 2 2 1

acute acute acute healing acute acute acute

3

acute

3 2 3 1 1 1 2 2 1 1 1 3 2 0 2

acute acute acute acute acute acute acute acute acute acute acute acute acute acute acute

1

acute

2 2 2 3


Pericarditis. Lost original record. 1

1

Clipped X & Y. Lost original record. baseline wand. Lost original record.

1

Z distorted. baseline wand., spikes, poor quality. 1

1

X&Z distorted (clipped). spikes. Some distortion. Same than p15. X clipped. Myocarditis. Atrial fibriloflutter. Y spikes. Coronary atherosclerosis. Supravent. tachycardia. Same than p11.

1 1

1

Pericarditis, VF, Y weak. Same than p34. Ischemic cardiop. idem p18. Just 198 sec of data. Bad quality Vcm.

1 1

1

Bad quality Vcm.

1

1 1 1

1

X clipped. Z clipped. Atrial fibrilation, edema, cardiomegalia.

1

1

1

1 1

1

1

1

1

Pericarditis. X clipped. Same than p17. Ischemic cardiop.Y spikes. X baseline w., weak. X clipped, Y weak. just 225 sec of data. interf. X(H)&Z(M), X EMG(M). Z spikes.

258


ID p43 p44 p45 p46 p46b p48 p49 p50 p50b p51 p52 p53 p54 p54b p55 p56 p57 p57b p58 p59 p60 p60b p61 p62 m,C std,%

day MI days HBP diab ang 7 5 6

healing acute acute

1

3

acute

1

25 5

healing acute

1

4

acute

1

1

12 7 4

healing healing acute

1 1

1

10

healing

8 9

healing healing

7

healing

11 14

healing healing

11

healing

10 10 4.4 4.6

healing healing

multi PVC Other comments MI 1 Pericarditis.

1 Dilated myocardiopatia, pump fail. Alias. 1 1

1

Ischemic cardiop.

1

Ischemic cardiop. Y leads off. 1 Edema, septal ischemia.

1

1 Pump fail. Just 52 sec of data. Idem p54.

1

1

1 Y distorted. idem p57.

1 1

1

Marfan syndrome, ischemic cardiop.

1 X slightly clipped. 24 41

7 12

8 14

11 10 18.6 16.9

259

Appendix C. Healthy Volunteers

ID v01 v01b v02 v02b v03 v04 v04b v05 v05b v06 v07 v08 v09 v10 v11 v12 v13 v14 v15 v16 v16b v17 v18 v18b v19 v20 v21 v22 v23 v24 v25 v26 v27 v28 v29 v29b v30 v31 v32 v32b v33 v34 v35 v36 v37 v38 v38b v39 v40 v41

W

race B

1

A

sex wgt hgt ag. BMI blk PVC M F kg cm

Other comments Clipped. idem v01. Y dist. idem v02.

1

29 85 183 25.4

1

53 63 160 24.6

1

1

37 76 170 26.3

1

1

58 56 172 18.9

X&Y dist. idem v04.

1

1

28 74 178 23.4

Epileptic.

1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

38 31 50 43 47 77 56 64 73 48

1

1

62 82 165 30.1

1

1

49 65 164 24.2

1

1

57 60 163 22.6

1

1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1

1

1

1

1

54 55 50 67 79 60 95 70 95 55

175 170 163 174 170 166 174 170 173 175

168 174 157 174 169 175 181 170 189 166

21.2 22.5 21.1 25.4 24.2 22.1 24.4 30.8 25.1 28.1

19.1 18.2 20.3 22.1 27.7 19.6 29 24.2 26.6 20

1 1

Y dist. Y dist. Y dist. Y dist. Y dist. spikes, Y dist.

X&Z spikes.

1 Y dist.

1 X dist.(L) too much noise, spikes, X leads off. spikes. Y baseline w., Y&Z dist. spike, Y&Z dist. X spikes, Y dist. X spikes.

43 61 153 26.1

weird Y.

1

33 90 176 29.1 31 80 160 31.3

Y dist. Y&Z dist.

39 55 177 17.6

1

1

54 54 45 58 43

1

1

37 64 162 24.4

1 1 1

28 65 175 21.2 31 63 162 24 51 61 164 22.7

1 1

Y&Z dist.

1

1 1

1 1 1

23 56 43 36 40 37 37 51 46 48

65 65 56 77 70 61 74 89 75 86

1 1 1

65 60 80 77 47

190 151 170 178 162

260

18 26.3 27.7 24.3 17.9

Y dist. Pt shoulder, X&Y dist. distorted X, Y. Y dist. X contact noise..., Y&Z dist. idem v38. Z dist. Z distorted.

Appendix C. Healthy Volunteers

ID v42 v43 v44 v45 v46 v46b v47 v48 v49 v49b v50 v51 v52 v53 v54 v55 v56 v57 v58 v59 v60 v61 v62 v63 m,C std,%

W 1 1 1 1

race B

A

sex wgt hgt ag. BMI blk PVC M F kg cm 1 33 78 169 27.3 Z dist. 1 31 68 178 21.5 1 51 64 165 23.5 Z dist. 1 31 65 178 20.5

1

1

1 1

1

1

1

1

1 1

1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 54 86

30 78 168 27.6

9 14

0 0

Y&Z dist. idem v46.

54 47 163 17.7 23 68 165 25

Z dist.

18 50 163 18.8

X dist.

22 30 62 1 45 1 35 1 35 1 20 1 26 1 40 1 28 1 33 1 48 1 72 1 34 46 17 42 73 27 13

82 55 83 73 63 70 46 54 80 107 67 75 85 86 69 13

168 165 170 167 164 166 166 174 172 188 175 182 170 173 170 7.8

261

29.1 20.2 28.7 26.2 23.4 25.4 16.7 17.8 27 30.3 21.9 22.6 29.4 28.7 23.9 1 3 3.85 1.4 4.1

Other comments

Y&Z dist. Z dist. Y dist. Z dist. Z dist. Y dist. Z dist. Y dist. Y&Z dist. Y dist. Y dist.

262

n

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

p01 p02 p03 p03b p04 p05 p06 p07 p08 p08b p09 p09b p10 p10b p11 p12 p13 p14 p15 p15b p16 p17 p18 p18b p19 p20 p21 p22 p22b p23 p24 p25

X WC(dB)

ESB(Hz)

Pt

P60

P120

P180

P240

P300

P360

P420

P480

Palias

-10.0674 72.48653 557.7929 0.000155 6.15E-06 6.66E-06 7.92E-06 7.38E-06 1.37E-06 1.81E-06 6.28E-06 7.65E-06

-5.31911 -11.9956 -7.10453 -8.02045 -2.54707 -3.03516 -7.44823 -3.64955 -5.47869 -8.882 -9.94975 -4.128 -5.42211 -4.72594 -5.19971 -12.6776 -13.1394 -17.7143 -6.34771 -6.98767 -4.70007 -6.22025 -6.15587 -9.53386 -7.42973 -5.45969

60.27304 4.702939 56.65524 16.86937 137.6665 77.74392 13.83384 79.26238 37.99587 14.46457 44.3116 109.1976 84.27209 79.96545 88.22954 3.781951 3.924192 6.302808 22.26417 13.13869 87.11369 49.51132 73.34006 9.20531 59.32283 84.39103

29.20977 128.0598 31.80614 110.5447 93.17256 25.63873 48.88561 39.03284 209.5076 480.6776 137.5173 38.66543 100.0979 134.0505 49.34633 17.68286 230.2761 1344.084 23.01581 3182.207 83.60885 18.27688 19.88247 54.44893 77.53547 25.33983

9.429477 102.4896 5.496794 42.64206 7.716721 4.241046 25.72006 6.355596 57.80437 314.509 9.630259 5.246743 23.43671 37.35149 6.824376 14.08731 264.2859 1226.096 6.000233 2007.216 20.37209 5.456727 3.969198 44.2721 4.106366 4.439622

0.439362 0.84071 0.306646 1.002202 2.830984 0.5992 0.312296 0.475612 2.538741 3.14148 0.494741 0.509509 1.69995 2.08251 0.656985 0.026046 2.900864 1.869658 0.210518 17.99919 1.984603 0.149052 0.239339 0.53782 0.304931 0.275671

2.293628 3.664155 2.560105 1.351513 2.146274 3.063723 2.989779 2.128722 3.02934 3.315828 4.627139 3.676758 2.459484 2.270022 1.867673 0.831112 2.318077 3.574027 4.495928 13.12574 1.699987 1.803699 1.64123 2.2186 1.754478 1.228446

0.342619 0.236158 0.160847 0.580669 3.631855 0.821189 0.236254 0.441225 1.977512 2.103425 0.332247 0.469372 0.904005 1.498408 0.537424 0.026897 0.493077 0.645738 0.122136 24.0318 1.524466 0.14449 0.153651 0.174256 0.264333 0.174467

0.34803 0.556053 0.252182 0.71966 2.348189 0.646582 0.836678 0.909945 1.482265 1.670226 0.355291 0.558745 1.377779 8.176808 0.450766 0.070852 0.453787 0.498981 0.286398 19.96009 1.101859 0.308255 0.334402 0.218268 0.569472 0.154319

0.249195 0.145227 0.168525 0.25161 2.000837 0.486858 0.214368 0.471417 0.886809 1.120292 0.178148 0.19681 0.438168 0.652536 0.307292 0.017235 0.197716 0.267559 0.092616 12.01237 0.68937 0.094694 0.099788 0.103915 0.159492 0.157549

0.16366 0.079889 0.108278 0.18422 1.263607 0.319514 0.167259 0.206302 0.482848 0.617017 0.099579 0.136159 0.635743 2.567982 0.195087 0.011311 0.197453 0.220044 0.062005 6.673292 0.519609 0.071812 0.072711 0.082639 0.08105 0.093144

0.114643 0.065194 0.043664 0.143258 1.038742 0.277817 0.099226 0.173804 0.431458 0.477195 0.10043 0.22482 0.225944 0.324867 0.125214 0.007962 0.121474 0.179309 0.049183 6.881062 0.385924 0.050125 0.042662 0.065044 0.067895 0.060612

0.128684 0.08508 0.091663 0.128743 0.836174 0.225878 0.12502 0.210987 0.418942 0.538713 0.126435 0.20923 0.175529 0.330636 0.14157 0.013838 0.191585 0.168378 0.080752 6.775159 0.361187 0.05732 0.051892 0.073126 0.069894 0.092308

Appendix D. Noise characterisation of raw data

263

n

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

p26 p27 p28 p29 p30 p31 p32 p33 p34 p35 p36 p37 p38 p38b p39 p40 p41 p42 p43 p44 p45 p46 p46b p48 p49 p50 p50b p51 p52 p53 p54 p54b

WC(dB) -6.18996 -9.46265 -4.11128 -11.8527 -4.97405 -4.34498 -10.9834 -4.09609 -7.3351 -5.22138 -15.0588 -6.26968 -6.15168 -6.34357 -12.1326 -7.01513 -5.07046 -2.82339 -26.1019 -7.68654 -6.981 -3.22553 -4.46423 -15.7967 -7.23437 -11.0387 -12.3506 -7.91732 -7.31022 -6.59021 -9.46987 -7.7255

ESB(Hz) 26.69159 12.39895 70.61521 3.467751 117.4262 75.39193 5.325699 139.2219 11.18219 65.26512 3.052348 27.01517 16.02073 15.54846 6.454588 92.97503 45.6631 88.09644 2.439985 15.08895 13.70209 91.91457 121.0904 5.381918 53.28834 4.862541 4.043132 11.42115 28.13664 32.10544 6.875162 87.68843

Pt 51.36173 255.8295 81.77828 129.5007 23.06378 21.28953 93.01284 128.8088 48.35976 61.06316 66.45612 106.4166 51.71611 47.38937 1213.295 200.0363 101.2468 21.35258 4321.147 41.89871 534.6474 66.19059 188.3416 5503.031 589.1713 180.338 157.181 90.66613 47.52331 29.97265 95.98925 101.8152

P60 24.83084 127.0861 18.58943 123.295 2.54264 4.127108 63.48189 9.651229 24.39178 11.00213 66.87148 41.75287 30.4751 35.73553 1039.67 20.38146 41.41842 4.158301 4376.576 26.0989 360.5485 14.58027 19.24824 5150.783 18.73069 123.385 121.1204 49.16559 22.46024 10.83544 53.56885 9.002995

P120 0.563267 1.611526 1.061243 1.154196 0.22005 0.252803 0.294562 2.622147 0.343878 0.408039 0.222627 3.058545 2.299156 3.002774 20.44789 2.404652 2.11844 0.424431 2.44657 0.289299 6.438252 1.430469 2.249755 6.41389 0.408918 0.565821 0.278746 0.43924 0.42967 0.154207 0.306347 0.65358

X P180 P240 4.760561 0.466158 2.396441 1.045077 1.881768 1.373639 2.467874 0.496655 1.801111 0.240582 0.832388 0.225348 2.445327 0.241173 4.315388 2.420266 5.983831 0.330525 5.429325 0.626957 1.959987 0.083263 3.485804 1.985617 1.718913 1.233855 2.153482 1.494921 24.35972 10.32448 5.580149 1.253125 7.677768 2.385337 1.2821 0.609878 9.180096 0.2544 2.914889 0.258423 2.229569 1.480966 3.947138 1.476607 2.925686 1.729511 21.42336 3.735169 0.084223 0.808284 7.036562 0.35372 6.775805 0.256573 3.621991 0.409864 3.820128 0.359892 5.272612 0.190356 11.2358 0.195762 1.073639 0.282631

P300 0.724368 0.621699 0.882438 0.328289 0.262018 0.202668 0.174744 1.599671 0.624015 0.636609 0.153727 1.645091 0.613588 0.66116 41.2395 0.898469 0.960216 0.37109 0.359446 0.184221 1.245166 1.156692 4.040749 2.93249 0.603528 0.72993 0.692034 0.451955 0.496888 0.433217 0.921763 0.987166

P360 0.283462 0.44659 0.613929 0.258901 0.161395 0.189574 0.13799 0.972706 0.210697 0.305082 0.076683 0.283973 0.21999 0.204336 1.112021 0.548586 0.590806 0.262387 0.261132 0.162009 2.558473 0.799885 7.899581 2.119049 0.116434 0.183519 0.140628 0.212075 0.157981 0.115752 0.197661 0.137749

P420 0.152474 0.254604 0.313892 0.174571 0.056546 0.076512 0.084672 0.47538 0.12814 0.194697 0.049006 0.52141 0.240346 0.322787 29.38343 0.31954 0.52466 0.132901 0.346628 0.088224 13.60325 0.65971 4.693447 1.640818 0.250268 0.213459 0.229999 0.18258 0.168142 0.086413 0.247672 0.374318

P480 0.10517 0.184704 0.201101 0.07937 0.054145 0.045907 0.057868 0.384999 0.092691 0.115934 0.030145 0.585591 0.21232 0.242498 1.669419 0.268795 0.334586 0.092214 0.094203 0.05606 31.86538 0.448398 1.838544 1.331835 0.376082 0.083644 0.075064 0.11801 0.090137 0.067098 0.120169 0.067653

Palias 0.122625 0.221397 0.278969 0.137008 0.078429 0.093018 0.080514 0.400984 0.109564 0.150842 0.047765 0.989462 0.169504 0.221215 16.08698 0.32776 0.37061 0.130945 0.198369 0.118229 28.9087 1.177741 0.95998 1.339974 0.37738 0.149038 0.113595 0.132079 0.108437 0.093913 0.233729 0.116062


n

ID

WC(dB) 65 p55 -5.08875 66 p56 -5.22165 67 p57 -4.81361 68 p57b -4.71531 69 p58 -9.93025 70 p59 -6.77955 71 p60 -8.79406 72 p60b -9.79668 73 p61 -17.9793 74 p62 -6.87192 75 v01 -9.55049 76 v01b -10.787 77 v02 -12.5408 78 v02b -10.9848 79 v03 -15.8131 80 v04 -11.2747 81 v04b -11.8298 82 v05 -9.68684 83 v05b -6.66078 84 v06 -11.4088 85 v07 -11.076 86 v08 -7.54718 87 v09 -5.45464 88 v10 -9.99998 89 v11 -6.20515 90 v12 -9.29177 91 v13 -9.31198 92 v14 -6.93306 93 v15 -8.30943 94 v16 -8.30577 95 v16b -6.56396 96 v17 -12.754

264

ESB(Hz) 45.59355 79.13544 46.80996 28.90323 5.493288 10.95778 10.28018 6.216839 2.817754 36.80833 4.293379 3.548334 4.563845 9.885639 3.255603 4.992653 4.353156 4.851009 8.909438 4.619637 3.925024 21.05482 10.60949 5.735636 86.73092 7.660996 11.40208 13.74221 10.77764 24.58697 63.94713 3.456377

Pt 57.53825 35.55835 90.6067 90.41459 49.73137 49.5948 116.7749 85.72474 339.1212 91.54046 119.2587 132.6313 104.9523 77.30082 128.79 104.4501 99.47133 113.9968 161.9304 87.5399 88.02182 75.97853 70.70365 114.36 162.0121 49.34514 62.90933 129.1223 46.49206 78.5116 66.33639 71.32048

P60 11.11622 4.461393 31.46111 30.74955 40.15325 28.11249 53.11356 71.57183 388.2899 31.69327 91.52809 105.1491 89.59678 54.64743 119.5063 80.99174 99.99836 69.91421 106.9261 57.7575 69.02909 15.08785 41.46084 63.91443 18.20137 26.58504 32.074 64.07269 22.93201 25.83427 7.64762 63.85206

P120 4.69E-01 0.408831 1.040127 0.886961 0.197138 0.479964 0.549735 0.473516 0.416196 1.116549 0.333752 0.232932 0.233391 0.202615 0.096831 0.396343 0.54185 0.804447 1.828665 0.155072 0.232676 0.294787 0.853309 0.413142 2.46459 0.212888 0.340078 2.5362 0.301631 0.578866 0.516381 0.117939

X P180 P240 1.76E+00 5.65E-01 0.823696 0.39997 2.157789 1.039219 3.931434 1.189368 2.641724 0.167563 1.830574 0.316573 2.596069 0.400409 3.262318 0.381092 3.952224 0.174187 2.216065 0.695035 0.983857 0.320065 1.577443 0.268215 3.625303 0.176142 3.894673 0.143799 6.234672 0.083056 4.167912 0.27877 2.917351 0.268443 4.167259 0.481206 4.786944 1.837727 2.811796 0.130571 2.706418 0.243926 3.064733 0.228403 3.664522 1.040095 2.665323 0.296536 2.883071 1.018944 2.15472 0.149398 2.515574 0.234807 4.478801 1.172011 2.906674 0.199329 5.687668 0.446232 4.503015 0.465739 3.788997 0.142218

P300 4.36E-01 0.381593 0.936136 1.114635 0.227975 0.321618 0.806657 0.871867 0.573257 1.240216 1.27744 1.132707 0.747918 0.196257 0.344102 0.3068 0.250563 0.377557 1.427964 0.24376 0.288346 0.259305 0.85367 0.374937 0.85101 0.219956 0.248603 0.770361 0.229324 0.480344 0.537364 0.201266

P360 2.92E-01 0.21805 0.514596 0.73013 0.090423 0.188616 0.183059 0.183719 0.108137 0.380743 0.248266 0.232356 0.121747 0.098206 0.100498 0.139859 0.147456 0.180163 0.649808 0.115118 0.150699 0.142787 0.504878 0.16501 0.460029 0.111302 0.120394 0.357685 0.114527 0.248898 0.282229 0.105724

P420 2.23E-01 0.130109 0.814288 0.47379 0.308208 0.205459 0.169161 0.211419 1.520225 0.295811 0.32461 0.248331 0.102467 0.063674 0.044171 0.096161 0.092976 0.088754 0.298476 0.054687 0.063458 0.077878 0.286901 0.084141 0.283031 0.059646 0.087885 0.212523 0.0736 0.1702 0.164357 0.050631

P480 1.19E-01 0.088555 0.312334 0.294193 0.053135 0.086951 0.085462 0.076901 0.058417 0.160458 0.178008 0.194213 0.046974 0.040976 0.033803 0.059418 0.054652 0.060021 0.244581 0.05094 0.052863 0.056265 0.201771 0.065738 0.20921 0.043475 0.06465 0.145089 0.055144 0.133213 0.130577 0.038302

Palias 1.57E-01 0.122977 0.391873 0.339383 0.219041 0.128514 0.116843 0.247157 0.168005 0.201648 0.205584 0.246824 0.055921 0.067935 0.091176 0.078347 0.100125 0.121631 0.25262 0.08751 0.094931 0.078674 0.226571 0.118547 0.237038 0.062013 0.084581 0.189623 0.071121 0.14377 0.139806 0.073764


265

n

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128

v18 v18b v19 v20 v21 v22 v23 v24 v25 v26 v27 v28 v29 v29b v30 v31 v32 v32b v33 v34 v35 v36 v37 v38 v38b v39 v40 v41 v42 v43 v44 v45

WC(dB) -10.3009 -9.57963 -8.10849 -8.88073 -6.4747 -7.13356 -6.33952 -4.79278 -4.98498 -7.63074 -8.21369 -6.75099 -8.55337 -6.23019 -6.4139 -7.36455 -6.07032 -5.80231 -3.14294 -7.07578 -6.3613 -7.75583 -6.07406 -5.42099 -5.65664 -7.31995 -4.86939 -7.08649 -4.29413 -10.1973 -4.6469 -7.29557

ESB(Hz) 3.549415 4.857276 10.53882 6.634883 11.68485 12.5404 45.30978 20.58129 54.81884 19.14217 15.04509 7.78786 9.644406 38.39816 27.87125 35.25114 34.60788 62.81955 127.2319 12.01159 12.91595 23.79769 89.90134 29.31511 37.0712 25.05607 60.4829 11.75628 63.2184 5.231506 63.17973 8.821593

Pt 93.19465 67.36218 68.26831 72.20154 160.2267 58.94526 18.80146 99.6991 35.00711 60.5275 35.55541 64.57338 75.62527 47.98949 58.03389 46.74753 97.5152 118.1144 81.42199 70.20468 86.72308 66.40551 188.4788 119.7235 100.2355 91.23505 84.72148 98.98095 36.41172 92.50717 72.8571 99.33546

P60 76.77849 77.96569 29.94173 37.67027 67.95922 27.02716 5.779628 39.65239 9.627635 20.37643 13.59879 32.05569 40.34639 18.3415 21.05115 11.71092 25.32277 28.78129 7.475215 28.02691 41.60173 21.19833 5.733164 38.99564 34.53005 29.44746 10.99013 51.07057 8.647922 68.19793 15.1779 37.13333

P120 0.548431 0.361559 0.368942 0.365499 1.337525 0.374749 0.147858 1.488597 0.463315 0.392434 0.159241 0.382494 0.39433 0.373732 0.349498 0.365503 0.701886 1.473061 0.863784 0.450919 1.116322 0.379171 0.865749 0.971114 0.991986 0.501145 0.678313 0.935426 0.487981 0.401411 1.279586 0.59349

X P180 P240 2.066205 0.452632 2.16662 0.348716 2.0105 0.322772 2.852346 0.29513 3.731118 1.486953 3.921067 0.408938 3.225627 0.14433 4.304261 1.475035 2.79061 0.466661 3.940314 0.295445 5.343197 0.134357 5.275922 0.524102 1.804418 0.287181 1.483362 0.363052 3.408687 0.357025 3.269657 0.294879 2.812297 0.678543 4.031102 1.499791 4.544305 1.14201 3.369453 0.40456 3.395383 1.089034 4.918856 0.278238 3.695417 0.684557 3.817907 1.400493 3.229121 1.256527 3.375152 0.422414 2.813553 0.653239 3.873634 0.743007 2.824258 0.505501 3.017585 0.332269 4.716151 1.130825 2.369208 0.445855

P300 0.417159 0.337822 0.226937 0.270631 1.350926 0.378524 0.313462 1.060526 0.355471 0.289424 0.440771 0.528392 0.556952 0.589422 0.992395 0.488635 0.922637 1.202811 1.22769 0.908484 1.772382 0.840545 0.621961 1.310491 1.935896 0.95108 0.617951 1.155867 0.602838 0.518177 1.046242 0.57042

P360 0.177875 0.214184 0.173623 0.151797 0.568795 0.153263 0.077767 0.500259 0.185646 0.12231 0.087897 0.26964 0.1447 0.185335 0.1724 0.105696 0.261168 0.468357 0.53555 0.189405 0.289863 0.154733 0.246007 0.770793 0.483811 0.226226 0.244112 0.26911 0.234119 0.113126 0.374053 0.20946

P420 0.092388 0.125823 0.104518 0.076805 0.293677 0.102364 0.072103 0.2775 0.102013 0.066733 0.081903 0.177038 0.115145 0.145983 0.159115 0.10951 0.201481 0.296713 0.349713 0.196803 1.526891 0.139826 0.177917 0.426434 0.3983 0.172739 0.157399 0.208057 0.169936 0.116515 0.272349 0.183895

P480 0.06567 0.103806 0.066909 0.051748 0.199576 0.056551 0.04086 0.188176 0.080405 0.051001 0.048496 0.134935 0.063288 0.088454 0.08944 0.043663 0.09998 0.177777 0.187006 0.094241 0.192274 0.087885 0.112168 0.219686 0.198818 0.097647 0.117248 0.103948 0.098657 0.051387 0.149103 0.098794

Palias 0.138196 0.160875 0.095542 0.077443 0.232262 0.087623 0.049136 0.223726 0.085329 0.070512 0.047824 0.135527 0.08436 0.098542 0.094703 0.069027 0.131716 0.224598 0.243876 0.098931 0.189046 0.084032 0.120022 0.292321 0.222519 0.111035 0.102204 0.106041 0.098864 0.063797 0.163435 0.10829


n 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

266

ID

WC(dB) v46 -7.13223 v46b -7.30677 v47 -7.49736 v48 -5.76345 v49 -6.214 v49b -5.89952 v50 -8.78887 v51 -5.5575 v52 -7.7278 v53 -7.413 v54 -3.86859 v55 -5.31378 v56 -5.68113 v57 -4.97754 v58 -8.50676 v59 -11.1076 v60 -7.44402 v61 -7.7804 v62 -8.87248 v63 -8.12742 Ave. -7.89439 %

ESB(Hz) 13.98068 14.2544 24.06221 64.76394 10.8047 11.74932 67.97 18.03545 55.85558 15.54276 72.94585 74.67334 70.49794 25.25823 16.57319 4.743683 44.99983 52.51622 16.63566 62.76434 34.55686

Pt 33.71707 43.94668 102.3986 96.53203 35.28399 34.71695 82.71708 19.63996 39.49177 48.82779 44.46795 40.71881 29.04674 60.03214 36.20569 62.30911 31.22959 35.99189 30.12298 78.11693 223.3358

P60 15.08165 20.28857 21.52324 13.68442 17.40211 22.60746 12.77177 8.09312 8.605997 20.07801 8.155562 9.295298 6.697225 27.39259 14.89808 48.2747 2.580599 4.716764 12.2483 7.877389 155.8023 69.76145

P120 0.243739 0.289681 0.526863 0.678557 0.281058 0.359528 0.788187 0.252283 0.185585 0.226905 0.577534 0.489302 0.229847 0.945885 0.174218 0.226123 0.178065 0.163725 0.095405 0.629749 1.209508 0.541565

X P180 P240 3.170048 0.200024 2.456299 0.211351 3.589131 0.313537 4.236957 0.844539 2.734298 0.325768 2.107777 0.476853 2.082248 0.274653 1.66385 0.207412 3.837341 0.145749 2.440962 0.211336 2.964876 0.790174 2.603029 0.500469 2.282663 0.245389 3.556502 1.023005 4.087146 0.106496 4.25814 0.163448 4.926129 0.06826 6.060249 0.107886 4.094012 0.08061 4.366965 0.268141 3.638155 0.936582 1.629007 0.41936

P300 0.431818 0.517518 0.347563 0.771418 0.399243 0.524788 0.346645 0.236448 0.310532 0.391477 0.741837 0.560444 0.336875 0.699131 0.397815 0.494049 0.360694 0.578342 0.308545 0.236578 1.260041 0.564191

P360 0.112506 0.119815 0.123748 0.329668 0.161649 0.204534 0.102039 0.080009 0.085082 0.10785 0.370227 0.192799 0.112847 0.375636 0.06831 0.087201 0.06259 0.069616 0.076441 0.113689 0.481953 0.215797

P420 0.112908 0.09616 0.086833 0.168483 0.105009 0.151387 0.161568 0.071959 0.064687 0.076835 0.228909 0.143898 0.05459 0.19564 0.062709 0.076261 0.086752 0.201737 0.085851 0.186415 0.694303 0.310878

P480 0.049728 0.049116 0.05831 0.134913 0.062514 0.096097 0.051674 0.032114 0.038468 0.052638 0.173261 0.103082 0.040299 0.154463 0.028604 0.033817 0.021923 0.024102 0.028779 0.049505 0.485257 0.217277

Palias 0.051535 0.061636 0.071378 0.155118 0.081507 0.101612 0.071163 0.051312 0.065068 0.071612 0.180635 0.121792 0.056082 0.169008 0.052278 0.0565 0.039508 0.047478 0.063757 0.124112 0.603521 0.27023


267

n

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


Y WC(dB)

ESB(Hz)

Pt

-6.03758

56.8449 91.99738 3.705371 0.848135 0.979199 1.122772 0.602984 0.432607 0.313918 0.198151 0.201026

-11.3467 -8.89999 -7.63068 -19.0458 -4.62315 -12.6239 -6.5509 -4.48177 -5.51515 -9.99872 -6.82682 -6.20683 -4.87844 -5.02984 -5.72799 -11.0234 -5.91168 -16.3573 -11.6024 -19.6695 -8.57718 -21.5384 -17.2737 -7.6275 -4.22497 -4.65832

5.028139 27.60251 8.855848 2.949311 74.31382 3.611959 44.12949 43.78605 98.53638 4.338944 58.07221 50.14112 69.68217 72.73097 64.17771 4.089925 48.42066 3.091002 7.65154 2.713761 7.44637 2.562125 5.040466 42.09352 106.1379 129.3232

85.21854 73.86402 56.37796 979.254 25.86578 95.96021 47.59908 55.64294 105.0503 418.0526 27.89965 49.95015 62.15684 61.42621 40.23766 129.3903 22.29951 256.2355 714.2117 21411.85 129.8932 2955.94 1951.87 51.52142 73.77534 11.98325

P60

53.25579 5.367734 28.52568 798.2631 6.684031 84.46787 15.94561 15.56538 12.05891 489.0534 2.891837 13.50168 16.81732 15.20461 10.30726 113.5762 7.41406 231.63 510.3038 20042.71 100.9416 2557.945 1882.843 21.87419 5.411663 2.015718

P120

0.483177 0.364664 0.643429 11.0595 0.560121 0.678637 0.937764 1.541926 1.375282 2.643648 0.151187 0.855941 1.24991 1.12758 0.450601 0.79547 0.338944 0.48847 17.82275 8.421402 2.319549 1.096843 2.747819 1.680484 0.57922 0.222008

P180

3.760154 3.481687 3.782262 1.172929 1.165618 3.401993 2.493821 3.511676 3.158983 4.295821 2.766348 2.322355 2.102889 2.498533 2.316419 4.41019 3.762009 4.983063 6.728028 8.721896 3.235038 5.235246 5.643251 2.547618 4.300016 0.779043

P240

0.232931 0.352248 0.296623 0.410295 0.490302 0.323206 0.288501 0.648934 0.775981 2.320356 0.204025 0.397879 0.709858 0.55838 0.344524 0.49138 0.219961 0.18391 1.536219 7.332972 0.920998 0.538915 0.922532 0.295025 0.646224 0.195692

P300

0.236406 0.30954 0.328053 0.23884 0.43831 0.354447 0.261669 0.628283 0.548607 1.876883 0.281651 0.276988 0.645625 0.470976 0.232502 0.362447 0.264819 0.249431 0.921144 5.734806 0.449736 0.750845 0.734792 0.179533 0.587632 0.347648

P360

0.104059 0.190171 0.184819 0.135088 0.360869 0.196372 0.137632 0.34555 0.301426 1.07969 0.076272 0.16169 0.288572 0.237755 0.169863 0.147167 0.071647 0.077212 0.441373 3.543898 0.314155 0.27718 0.402255 0.078749 0.32176 0.045172

P420

0.099337 0.106927 0.158954 0.144821 0.289075 0.156228 0.080027 0.174182 0.205052 0.661033 0.052309 0.097208 0.22047 0.209713 0.103202 0.088241 0.058354 0.055678 0.343594 2.308798 0.260151 0.200104 0.295467 0.055015 0.215552 0.046344

P480

0.04626 0.120895 0.098521 0.160038 0.220896 0.129015 0.052681 0.145279 0.138865 0.51367 0.03917 0.071996 0.137229 0.114382 0.087818 0.060245 0.034543 0.041107 0.293857 1.950241 0.149712 0.107658 0.269051 0.064781 0.174881 0.03257

Palias

0.115369 0.14069 0.139532 0.150191 0.213196 0.134096 0.086466 0.155265 0.184993 0.531989 0.065254 0.09884 0.160458 0.128329 0.117675 0.085907 0.046186 0.0632 0.316718 2.032986 0.142381 0.16249 0.295772 0.075574 0.180919 0.084356


268

n

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64


WC(dB) -12.4173 -6.73092 -9.85276 -17.3564 -6.23819 -7.50853 -8.12955 -4.71034 -15.2563 -6.10273 -12.4486 -7.94374 -6.24091 -4.17545 -6.16361 -3.7148 -4.65503 -4.72032 -26.6717 -5.88094 -6.37686 -7.16454 -5.81911 -11.1496 -2.83418 -11.4854 -12.6423 -4.71632 -8.71245 -9.40363 -4.47573 -8.16507

ESB(Hz) 6.177648 84.93204 7.128934 2.766441 79.03209 19.58457 17.75569 116.4436 4.168864 31.05707 3.989812 79.44794 34.94573 38.15963 79.60527 50.36506 143.9318 82.58469 2.465689 44.80043 65.73513 8.853394 14.87562 6.785794 189.1999 4.316249 4.027468 121.6946 12.86772 5.989526 40.37412 7.161802

Pt 380.6995 129.6491 322.8529 304.8119 35.63547 16.07849 37.6151 140.9687 516.5944 136.9947 41.40571 105.9412 39.11826 21.82037 45.61124 113.2829 69.57467 27.2032 5672.244 34.38033 141.5855 226.6541 236.0303 771.2107 238.5387 195.8351 152.8309 19.6509 36.01836 66.02486 21.29653 40.60894

P60 368.8748 29.73876 216.9358 322.164 8.159258 7.8552 23.81625 23.02013 401.4419 42.97585 37.16618 8.166449 7.630017 6.585274 7.586157 28.42299 9.466789 6.463851 6093.753 11.29559 32.37357 137.0453 93.67507 625.6494 17.45055 168.4479 117.9213 3.028881 15.97404 40.04585 7.116149 33.39335

P120 3.149065 1.946794 1.671984 1.656233 0.353598 0.077898 0.218174 3.231518 0.820526 2.402225 0.196039 1.117402 0.391168 0.365484 0.321678 2.070613 1.479232 0.65386 4.421236 0.579556 1.209275 1.920077 1.263784 4.011953 7.041093 0.619687 0.336538 0.374873 0.213742 0.282623 0.340447 0.603115

Y P180 P240 3.086603 1.094445 5.675737 0.995041 2.596199 1.180217 3.012739 0.40853 2.229991 0.228745 2.005401 0.057577 2.258138 0.174659 6.110505 1.715573 3.505765 0.319926 3.027575 1.240162 1.856729 0.064559 4.260639 0.52036 2.632145 0.238742 2.137199 0.327753 2.05049 0.275556 2.707689 2.149987 3.047158 1.14115 2.866947 0.469051 59.07534 0.288277 2.955809 0.252919 2.052588 0.582141 4.282843 1.668651 4.719103 0.958153 3.866065 2.07387 4.98243 5.968921 3.594769 0.479071 3.774664 0.249463 0.850701 0.154302 1.431033 0.1522 0.997552 0.237773 2.198219 0.234951 1.848798 0.267444

P300 0.771249 0.757062 0.711741 0.110035 0.195809 0.12003 0.236816 1.514346 0.391456 0.481408 0.08893 0.376984 0.149661 0.22014 0.332257 1.44546 0.749007 0.337439 1.942509 0.341006 0.373078 0.724455 0.972847 1.280144 14.65371 0.404123 0.222868 0.145886 0.10683 0.200359 2.147869 0.940188

P360 0.32731 0.417422 0.489065 0.113633 0.09561 0.0559 0.088959 0.798356 0.186983 0.414761 0.055089 0.188194 0.086477 0.16567 0.134345 0.80937 0.362291 0.191801 0.217167 0.098118 0.360905 0.514435 4.266167 0.769401 3.240994 0.205062 0.106253 0.075907 0.059465 0.098525 0.200364 0.096624

P420 0.212829 0.293501 0.277803 0.104112 0.069128 0.049065 0.091276 0.529959 0.120675 0.358696 0.045162 0.117367 0.05729 0.103693 0.104523 0.519852 0.289849 0.094535 1.168625 0.113572 2.053246 0.635975 6.680704 0.520172 1.318593 0.253645 0.171481 0.064222 0.047026 0.108451 0.29227 0.081539

P480 0.170721 0.213119 0.222629 0.051293 0.037823 0.018571 0.044603 0.433411 0.099497 0.400996 0.024191 0.084798 0.042918 0.085682 0.081523 0.421847 0.167745 0.07348 0.098567 0.039209 27.84822 0.372059 0.505122 0.325959 1.101055 0.094267 0.055594 0.04656 0.032803 0.051617 0.125277 0.040746

Palias 0.234268 0.234719 0.263282 0.123378 0.063463 0.040437 0.078909 0.440389 0.125742 0.269704 0.041386 0.125873 0.072133 0.121125 0.081873 0.48701 0.229123 0.119699 0.461431 0.06595 10.73167 2.031736 0.451666 0.391716 1.491671 0.197499 0.163879 0.046488 0.052407 0.06416 0.0967 0.066371


n

ID


269

ESB(Hz) 23.93446 5.401326 31.15308 34.78807 4.159655 16.14075 28.00552 8.1886 5.498701 25.96846 3.59076 2.861066 3.8645 3.661034 3.052476 97.47048 14.08435 6.068847 18.17203 10.58591 6.240206 7.512801 30.41997 6.782324 14.09026 4.304838 4.030146 5.07997 12.20996 3.38773 4.590279 3.082778

Pt 94.56843 1186.59 150.5637 138.4839 133.1274 66.5695 66.52335 66.61144 120.3824 99.40464 114.8319 169.8938 78.76513 92.867 82.50392 225.7395 66.55421 100.0221 111.291 95.92953 120.6468 51.07996 257.9635 150.2709 136.7417 90.10579 124.728 197.0243 150.7466 423.3751 545.632 52.9865

P60 30.39032 983.8059 49.10971 44.58795 106.264 31.48509 22.91888 42.12822 73.83307 29.56321 108.176 155.7401 69.09815 75.52044 78.45451 29.66021 34.62684 54.35035 45.46682 44.18202 78.28394 24.2441 92.50368 90.14884 69.20606 64.39541 107.536 133.6068 70.36526 353.0067 374.4382 46.88395

P120 0.78836 1.127906 1.456648 1.549349 0.360036 0.847425 0.663264 0.452002 0.370954 0.942023 0.529265 0.330155 0.315867 0.15978 0.085228 5.433123 0.703684 0.562629 1.540552 0.230202 1.563532 0.311443 6.487576 1.390448 2.456171 0.272585 0.389267 1.785943 1.053893 2.129717 4.57234 0.163328

Y P180 P240 12.16898 0.532482 1.176213 0.461033 6.798712 0.92334 6.372545 0.717738 3.220656 0.312937 2.971233 0.514626 2.331088 0.374939 3.130649 0.323839 8.330503 0.1532 0.877521 0.575599 2.720946 0.256803 2.725876 0.169174 3.920628 0.157827 2.910427 0.100839 2.900594 0.071723 2.658979 1.123901 2.002704 0.341413 1.788157 0.311985 1.920011 0.770694 1.576089 0.243405 2.81782 0.873013 2.004776 0.307209 4.556975 3.657602 1.883702 0.495058 2.798541 1.099281 2.358422 0.122139 3.081755 0.180376 3.162627 1.108698 3.114167 0.392519 2.703828 1.631246 4.169981 2.948677 1.898243 0.095697

P300 1.353229 1.436776 0.810204 0.946461 1.496946 0.406272 0.638235 0.632853 1.576618 0.814753 0.195481 0.133856 0.090718 0.547506 0.506833 1.057225 0.428209 0.538958 0.862935 0.463545 0.622928 0.298193 2.722787 0.833925 0.902642 0.393 1.058853 1.009392 0.688268 0.792137 1.922783 0.16224

P360 0.233585 0.355766 0.342001 0.283422 0.11842 0.197492 0.121257 0.134958 0.060896 0.224015 0.117371 0.100621 0.073676 0.055584 0.050378 0.266541 0.117803 0.102229 0.268724 0.122298 0.154112 0.099386 1.122534 0.16671 0.404502 0.059069 0.083797 0.2902 0.156893 0.271428 0.744146 0.02504

P420 0.27879 0.669495 1.705342 1.972892 0.180366 0.258299 0.083196 0.186706 0.60286 0.138216 0.174927 0.089462 0.071683 0.05443 0.047657 0.204401 0.127805 0.171134 0.303409 0.162428 0.163218 0.120091 0.592957 0.235014 0.269378 0.114613 0.218804 0.258277 0.196559 0.143386 0.594176 0.049571

P480 0.106801 0.269841 0.160147 0.163038 0.057036 0.101143 0.057606 0.062469 0.032266 0.098879 0.086204 0.093179 0.041655 0.032842 0.026608 0.181192 0.062781 0.043636 0.108792 0.067295 0.064843 0.04222 0.382708 0.088785 0.146369 0.029402 0.041664 0.131261 0.075118 0.118573 0.412542 0.01174

Palias 0.127971 0.335082 0.199187 0.321761 0.129 0.240401 0.100805 0.147896 0.048148 0.16461 0.115108 0.190597 0.086068 0.047579 0.043683 0.135996 0.068286 0.052878 0.118714 0.084378 0.077398 0.056581 0.410803 0.103379 0.169069 0.044208 0.068531 0.143893 0.102602 0.135209 0.470015 0.026999


270

n

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128


WC(dB) -9.64772 -8.49988 -12.2745 -8.21667 -9.79754 -8.53535 -8.37086 -6.86798 -4.6212 -9.30702 -6.29201 -6.78104 -6.13007 -5.37672 -7.82214 -5.99711 -5.68405 -5.81161 -6.81408 -4.90143 -6.29427 -5.08209 -8.02866 -7.18367 -10.5315 -4.26712 -5.84946 -6.43686 -8.91534 -6.2557 -4.71142 -5.44296

ESB(Hz) 6.030677 7.866159 3.437285 11.18918 4.868996 18.18037 10.94266 18.79475 146.0674 50.4825 45.56742 10.66808 100.7509 67.60776 39.77136 111.5629 81.71285 85.67925 23.65568 129.3428 92.50015 117.7138 10.09375 13.37626 6.232289 126.8653 27.00041 24.05356 24.50218 44.85168 166.5177 80.29743

Pt 75.94883 81.44695 148.4155 81.53615 236.5768 52.85195 20.74182 121.7469 74.79361 98.63161 44.80129 21.10393 33.83663 45.81289 50.77686 50.22886 34.33723 47.51337 177.7142 34.17644 111.7787 37.19783 218.0729 118.9834 506.5372 77.52422 95.7191 60.04843 127.8596 44.30494 82.19454 45.80775

P60 46.90943 55.26263 111.0943 40.84863 159.8988 13.36461 13.61272 61.11742 5.884237 18.90698 7.857285 7.782655 4.942265 7.78864 17.65628 3.818138 4.916994 8.267603 43.67632 4.121658 17.12425 1.558122 50.67422 52.32888 405.4674 11.80837 18.15625 18.91867 29.5676 21.07065 5.144478 6.338929

P120 0.554169 0.744005 0.628333 0.740119 1.495422 0.23943 0.149203 2.252042 2.482161 0.705458 0.674369 0.117944 0.667379 0.849175 0.581926 0.839632 0.607705 1.024095 1.319503 0.959251 2.67559 0.589594 1.189319 1.772126 6.819071 2.273567 0.985946 0.754185 0.548774 1.229452 2.383265 0.512962

Y P180 P240 2.516211 0.239832 2.622334 0.396961 2.955933 0.316495 1.693393 0.422118 3.276372 0.961848 1.406048 0.115671 1.219373 0.089314 3.255796 1.18209 2.283663 1.540421 2.466171 0.300381 3.424035 0.34019 1.930717 0.117798 1.173745 0.232039 1.307011 0.399961 1.623399 0.332376 2.409997 0.490802 1.960949 0.264846 2.51255 0.464712 16.3038 1.207157 2.286581 0.670013 2.359101 0.894137 2.45605 0.330541 1.622182 0.62719 1.587158 0.784754 50.80659 10.61394 3.138315 1.719549 2.1077 0.711046 1.650016 0.446497 2.333712 0.307448 1.793697 0.510778 2.518785 1.097225 1.811356 0.593269

P300 0.386965 0.462433 0.690803 0.419018 1.073125 0.10493 0.11521 0.629913 0.806371 0.404882 0.176976 0.10513 0.1636 0.20234 0.197763 0.460905 0.261483 0.385016 1.831439 0.595943 0.514977 0.355377 0.289753 0.435414 46.32711 0.856807 0.310037 0.268925 0.367296 0.366271 0.661788 0.411212

P360 0.076843 0.153409 0.111986 0.133091 0.322942 0.04817 0.041573 0.351996 0.308256 0.106262 0.0729 0.063124 0.080152 0.128377 0.085801 0.128502 0.071537 0.146289 0.198633 0.244871 0.2259 0.103462 0.180401 0.223474 0.491777 0.464663 0.159774 0.149465 0.122022 0.167951 0.320348 0.173775

P420 0.107111 0.152083 0.09382 0.095315 0.239251 0.067096 0.059931 0.197381 0.2236 0.181714 0.077402 0.066419 0.060145 0.085658 0.065084 0.071775 0.042454 0.086999 1.056519 0.122206 0.17294 0.075093 0.15146 0.175455 22.37515 0.212433 0.095096 0.084643 0.074669 0.101728 0.177459 0.140082

P480 0.040826 0.065826 0.054162 0.052971 0.152505 0.023502 0.023957 0.122336 0.150745 0.054313 0.034378 0.032461 0.045393 0.060496 0.048694 0.050514 0.033712 0.060761 0.178305 0.099693 0.107706 0.055621 0.08552 0.10769 0.910436 0.148275 0.065678 0.066899 0.055762 0.061485 0.127612 0.1147

Palias 0.046426 0.076648 0.10234 0.104004 0.190179 0.036752 0.036228 0.143431 0.136551 0.061644 0.076098 0.054799 0.066902 0.090083 0.05945 0.077515 0.063024 0.094858 0.489306 0.111442 0.150363 0.072138 0.090851 0.101876 3.855434 0.176261 0.080921 0.073224 0.101081 0.073012 0.14719 0.118327


n 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

271

ID


ESB(Hz) 6.15054 6.506888 124.2174 6.724846 11.86493 68.63475 138.6447 140.5195 66.45172 81.28013 110.0869 94.45788 19.3518 47.93186 58.11114 16.99412 13.00829 5.427812 13.95556 71.0934 37.23638

Pt 74.83321 89.53287 155.1182 130.3144 45.52329 22.56397 25.60051 18.73205 24.81753 22.48881 89.12895 33.76157 27.23092 38.60175 33.29872 22.94981 15.51076 60.09713 16.51072 19.87131 395.328

P60 48.10896 47.33354 16.06839 66.28482 18.61214 6.512822 1.196406 3.020948 4.087901 3.217028 5.464948 6.365198 11.92551 9.136346 3.378305 7.759237 5.309703 38.40207 5.981208 3.555405 330.1605 83.51559

P120 0.675005 0.596768 3.579687 0.726154 0.445901 0.495292 0.322968 0.532391 0.222601 0.271165 1.370242 0.628826 0.287216 0.431847 0.204826 0.221746 0.107305 0.2146 0.083779 0.275724 1.515249 0.383289

Y P180 P240 1.841104 0.389498 1.464118 0.351642 2.972122 0.762962 6.16703 0.575197 4.760579 0.272339 2.076229 0.462598 2.483878 0.233857 1.18092 0.285791 2.882621 0.181073 2.190305 0.214141 3.001556 1.152891 2.274548 0.686343 3.22317 0.206915 3.617361 0.60011 3.284985 0.103402 3.746966 0.144415 3.450455 0.078701 6.088168 0.116938 3.227753 0.056326 2.856508 0.206075 3.927104 0.801538 0.993379 0.202753

P300 0.316974 0.475847 0.431284 0.710306 0.202873 0.339557 0.287051 0.100245 0.15223 0.142972 0.836774 0.591149 0.210647 0.399534 0.089701 0.084967 0.043573 0.245232 0.117959 0.186039 1.121462 0.283679

P360 0.129594 0.130766 0.326842 0.250651 0.095928 0.165598 0.077129 0.090489 0.078699 0.077608 0.453292 0.324245 0.085798 0.262101 0.042846 0.047522 0.026995 0.042941 0.025896 0.081201 0.307466 0.077775

P420 0.108529 0.106867 0.205158 0.245602 0.15641 0.120772 0.060626 0.063208 0.065188 0.067138 0.239864 0.211021 0.06332 0.16075 0.052909 0.061573 0.019765 0.089026 0.069009 0.157186 0.495845 0.125426

P480 0.055139 0.06399 0.154727 0.124683 0.038621 0.074009 0.042027 0.038827 0.036486 0.038142 0.174312 0.177389 0.042877 0.096792 0.019996 0.021414 0.013114 0.018121 0.011737 0.033238 0.36784 0.093047

Palias 0.069881 0.068705 0.16277 0.148211 0.065314 0.104164 0.057488 0.057398 0.053118 0.068552 0.220414 0.240948 0.066775 0.139168 0.069214 0.079062 0.056241 0.05992 0.035361 0.049439 0.301377 0.076235


272

n

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


Z WC(dB)

ESB(Hz)

Pt

P60

P120

P180

P240

P300

P360

P420

P480

Palias

-8.34251 55.96934 115.0257 10.84329 0.787461 1.416243 0.400622 0.208004 0.180876 1.81E-06 0.120064 0.115736

-15.9887 -6.98388 -8.83281 -15.0252 -7.22068 -9.33563 -4.35284 -3.06388 -8.13651 -10.385 -13.5398 -5.76119 -6.05166 -6.12539 -3.7892 -7.00908 -9.30005 -18.4385 -12.6814 -29.9001 -6.57412 -10.2539 -10.6684 -5.19827 -3.89147 -10.1466

3.386678 27.93506 14.09272 3.590209 10.45194 4.8183 72.70467 100.7265 77.16108 4.624513 4.763783 62.4496 42.41253 46.74434 118.5345 21.42335 23.54172 2.983961 3.871947 2.545765 46.18106 13.38324 9.26976 87.68806 63.38619 15.58233

533.9401 32.47614 73.50369 269.74 73.5886 76.7857 12.95895 15.75283 302.4349 616.2886 269.5107 17.43974 145.8736 102.1737 26.41838 54.12088 102.9278 306.3565 68.5855 33363.1 112.5567 68.79482 70.78029 14.82721 29.65314 73.64941

326.7634 7.897652 33.56182 223.8477 49.01154 60.18514 3.140151 2.435815 20.60734 479.5284 192.8208 5.365313 46.1495 37.41983 3.107371 19.72069 61.14286 308.0387 57.92819 32108.56 34.72401 38.50561 40.38347 3.774757 6.068887 47.94544

2.764326 0.175502 0.612689 2.317711 3.298968 1.210121 0.159997 0.18389 1.95151 2.789271 0.564993 0.370056 1.798558 1.890788 0.41224 0.365243 0.842975 0.247607 0.384146 1.805193 1.727901 0.317102 0.187608 0.251831 0.310342 1.572096

5.692314 1.338142 1.897802 1.646746 2.801093 1.624665 1.827876 2.133855 3.328254 3.26106 1.976458 1.591997 2.111537 2.527836 1.7282 7.658567 3.488586 5.370237 1.212954 2.539506 3.146687 2.747537 2.306741 0.67233 1.888422 2.998681

0.775958 0.200325 0.249772 0.264864 1.725399 0.734678 0.098589 0.237213 0.899197 2.228694 0.280649 0.153319 0.845859 0.940455 0.404919 0.226789 0.295301 0.120774 0.09262 0.789348 0.748538 0.181701 0.137216 0.138394 0.35198 0.379381

0.347033 0.182779 0.271167 0.167206 1.346119 0.642004 0.115643 0.355802 0.55723 1.676733 0.23172 0.123575 0.685808 0.640078 0.343736 0.4603 0.337332 0.172762 0.097766 1.166225 0.444008 0.232781 0.199718 0.110038 0.287264 0.136222

0.137397 0.103198 0.161218 0.110204 0.989937 0.490092 0.08379 0.269955 0.413723 0.957534 0.151735 0.063088 0.497378 0.31957 0.227864 0.137997 0.17726 0.074037 0.056966 0.423925 0.373273 0.090396 0.062384 0.081352 0.225201 0.071602

0.16366 0.079889 0.108278 0.18422 1.263607 0.319514 0.167259 0.206302 0.482848 0.617017 0.099579 0.136159 0.635743 2.567982 0.195087 0.011311 0.197453 0.220044 0.062005 6.673292 0.519609 0.071812 0.072711 0.082639 0.08105 0.093144

0.086787 0.05607 0.105783 0.092949 0.714831 0.343893 0.058192 0.080573 0.191462 0.445513 0.119987 0.0523 0.277443 0.234257 0.119558 0.065487 0.115832 0.047788 0.036572 0.314117 0.212756 0.044091 0.034298 0.042707 0.13418 0.045628

0.17292 0.062882 0.097665 0.10247 0.534111 0.313232 0.121126 0.095585 0.221264 0.459976 0.130199 0.065669 0.299117 0.241089 0.130162 0.093392 0.17336 0.058822 0.050164 0.373119 0.212573 0.061887 0.050841 0.049529 0.15492 0.060596


273

n

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64


Z WC(dB) -5.75902 -8.26068 -11.3792 -16.1272 -4.21107 -11.7364 -4.08935 -4.20624 -11.7313 -4.52134 -7.31235 -6.04906 -7.81181 -6.07786 -9.91916 -3.19337 -4.49955 -3.95468 -24.3721 -4.19682 -6.71429 -3.54771 -3.21942 -16.428 -7.00361 -8.86693 -8.91288 -7.90464 -7.87074 -4.40453 -7.65245 -7.56304

ESB(Hz) 64.91589 29.4114 3.646256 7.0706 133.9329 5.307365 114.7149 122.5422 3.751464 106.9268 11.96152 78.39921 19.00776 24.49735 14.2793 118.2597 91.96407 88.69438 2.485124 80.39479 60.99044 145.6389 141.9759 3.694419 80.59996 7.839811 6.1391 58.665 54.78003 23.03275 12.56457 44.39678

Pt 28.67181 155.9528 229.4544 1107.756 8.271425 53.68011 14.1123 122.4773 162.5887 42.93805 12.16336 51.05826 50.90517 45.43307 122.9248 62.93732 36.58961 32.0568 8376.851 10.88756 209.6841 86.23289 102.8819 3938.134 1190.466 11.52939 11.8233 38.64605 71.09355 16.38726 90.42732 115.0537

P60 10.47685 64.51891 205.2989 1014.466 1.265428 41.12218 1.993303 10.25995 129.1927 4.903426 5.747496 13.11807 24.90695 18.94176 54.80819 10.12669 11.42735 6.011786 8235.027 0.978474 42.08227 8.533262 9.515261 3765.347 197.3035 7.548567 7.387087 10.52264 12.392 6.253638 42.45146 22.63899

P120 0.323247 1.014568 1.080692 6.813948 0.183947 0.336322 0.184441 2.641069 0.479431 0.657087 0.072146 0.938412 1.608337 1.241669 0.61644 1.468286 1.062708 0.315068 8.13484 0.151157 0.455685 1.452955 1.242008 3.771606 29.17002 0.060384 0.060476 0.319312 0.859733 0.168491 0.845329 0.687931

P180 2.245754 1.806502 2.905588 5.461408 0.647932 1.412564 1.105082 2.432365 3.168452 0.815609 1.108755 1.346072 5.097848 4.698589 2.319662 1.56475 2.535172 1.939483 37.25973 1.982575 1.236803 1.628369 2.298525 16.96772 15.25924 0.229341 0.278812 0.847144 1.253583 0.859692 6.370005 1.875624

P240 0.255635 0.747857 0.787557 1.408413 0.097376 0.119783 0.17184 1.960782 0.361947 0.516132 0.064454 0.584805 0.423287 0.55964 0.316609 1.344746 0.990936 0.376759 0.678213 0.120643 0.499763 2.269383 1.39579 2.917951 10.72661 0.045054 0.043123 0.150531 0.303332 0.203734 0.31612 0.227647

P300 0.223748 0.479324 0.546955 0.416696 0.075109 0.098272 0.173388 1.205636 0.28946 0.292347 0.078087 0.349907 0.261884 0.408636 0.538045 1.040893 0.652061 0.317334 1.357852 0.239523 0.375689 0.616311 0.732087 1.814746 17.80826 0.025963 0.031899 0.112656 0.228692 0.153334 1.170623 0.471132

P360 0.117315 0.323393 0.324609 0.316123 0.06853 0.075587 0.110055 0.978099 0.165984 0.176955 0.051019 0.214059 0.113686 0.19068 0.160058 0.715226 0.406552 0.28031 0.276817 0.058648 0.376153 0.524977 4.422659 1.42894 6.777455 0.021788 0.021917 0.098379 0.139079 0.102199 0.208883 0.092187

P420 0.152474 0.254604 0.313892 0.174571 0.056546 0.076512 0.084672 0.47538 0.12814 0.194697 0.049006 0.52141 0.240346 0.322787 29.38343 0.31954 0.52466 0.132901 0.346628 0.088224 13.60325 0.65971 4.693447 1.640818 0.250268 0.213459 0.229999 0.18258 0.168142 0.086413 0.247672 0.374318

P480 0.078501 0.185508 0.155734 0.222312 0.027787 0.033874 0.060736 0.328274 0.08626 0.102411 0.021108 0.099995 0.053898 0.094523 0.100918 0.280671 0.177848 0.118015 0.141687 0.023368 25.87067 0.414091 0.452979 0.760949 3.194762 0.013641 0.013337 0.073872 0.086948 0.059556 0.13831 0.055282

Palias 0.082157 0.194237 0.19327 0.261938 0.050069 0.046769 0.059708 0.414807 0.096739 0.116767 0.028676 0.123106 0.094984 0.149411 0.11855 0.289558 0.195252 0.164257 0.340421 0.047756 10.61404 2.166285 0.473207 0.84728 1.644232 0.018878 0.018194 0.076584 0.083543 0.075142 0.181962 0.06549


n

ID


274

Z ESB(Hz) 54.41645 3.441734 67.42145 132.6122 54.69492 145.5655 43.93649 41.02407 6.184709 133.9435 18.89238 19.37025 21.30266 12.33702 9.719277 4.496262 8.202462 13.93433 159.2823 9.807168 5.75721 68.79715 16.04292 63.27256 127.7551 6.09488 59.70823 34.38941 91.35944 3.015743 3.747957 6.476539

Pt 28.24594 213.8046 63.71121 16.21889 19.65452 26.94397 21.69793 27.8231 405.5903 426.6886 20.01973 23.57171 29.87231 33.60374 39.69482 95.23961 50.18795 42.27037 17.28703 25.96629 35.75287 173.41 58.59468 103.9993 178.831 48.15303 46.49471 67.02065 69.04947 364.0928 374.9443 13.21588

P60 7.192768 219.0018 13.63074 1.826618 5.816435 4.423795 7.309165 7.512638 378.4586 40.67809 10.01387 8.237887 12.7 17.02703 25.11449 74.69686 30.34346 9.85267 1.659126 12.94286 24.31319 12.08129 24.61132 16.52789 14.01331 27.87859 5.090727 18.05912 13.928 349.7846 304.3908 9.562554

P120 0.361622 0.574883 0.630728 0.199186 0.114522 0.383885 0.222816 0.318841 0.676683 13.12144 0.181447 0.121427 0.164872 0.119537 0.133876 0.426286 0.302195 0.220284 0.360752 0.130085 0.220102 1.154871 0.58256 1.559643 3.999346 0.242376 0.314343 1.099228 1.478221 0.588749 2.134827 0.063325

P180 4.005204 3.470957 0.920849 0.582605 1.060041 0.825804 0.48994 1.123099 1.753249 6.359743 1.779446 1.761721 1.599039 1.744636 2.067055 1.644742 1.141862 1.168098 0.895101 0.876168 0.924683 1.7593 1.379502 1.781925 1.878612 1.049493 0.991886 1.949063 1.703047 1.980026 2.996224 1.349273

P240 0.34109 0.55137 0.588662 0.328735 0.134929 0.651809 0.186145 0.259377 0.28558 3.358804 0.156946 0.118554 0.095853 0.078049 0.107193 0.168619 0.256216 0.168141 0.393969 0.118504 0.178539 0.835689 0.852466 0.711627 1.062027 0.137304 0.15438 0.603468 0.438052 0.662719 3.049614 0.059142

P300 0.945396 0.906291 0.789868 0.266692 0.471048 0.77188 0.832853 1.285402 0.179682 1.890708 0.171021 0.144603 0.108178 0.055088 0.153343 0.109651 0.170898 0.13667 0.275322 0.156906 0.123209 0.568506 0.598456 0.379423 0.570209 0.101904 0.099858 0.401379 0.273486 0.624367 2.175638 0.296733

P360 0.197982 0.341465 0.324229 0.160767 0.094779 0.428196 0.102326 0.120968 0.151365 0.849654 0.090227 0.092755 0.056773 0.04386 0.07199 0.071867 0.11703 0.070301 0.151925 0.075302 0.083432 0.350019 0.389507 0.214742 0.3434 0.059459 0.070711 0.264777 0.175145 0.368205 1.421274 0.042536

P420 2.23E-01 0.130109 0.814288 0.47379 0.308208 0.205459 0.169161 0.211419 1.520225 0.295811 0.32461 0.248331 0.102467 0.063674 0.044171 0.096161 0.092976 0.088754 0.298476 0.054687 0.063458 0.077878 0.286901 0.084141 0.283031 0.059646 0.087885 0.212523 0.0736 0.1702 0.164357 0.050631

P480 0.11759 0.204731 0.200225 0.100201 0.06108 0.229448 0.053782 0.083982 0.06743 0.388399 0.067543 0.085673 0.034063 0.029823 0.0453 0.045045 0.076556 0.028754 0.068334 0.049397 0.040763 0.154616 0.214758 0.094223 0.159093 0.036385 0.038203 0.138055 0.069972 0.21661 0.864939 0.022186

Palias 0.148815 0.198888 0.230205 0.156096 0.10158 0.237103 0.097636 0.209195 0.076318 0.442561 0.09905 0.161308 0.043164 0.040801 0.068894 0.056674 0.084451 0.051688 0.082377 0.062209 0.061224 0.190504 0.202773 0.102683 0.174772 0.045424 0.047314 0.153684 0.088941 0.2155 0.860543 0.02509


275

n

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128


Z WC(dB) -5.51582 -6.03354 -8.20474 -8.76688 -7.54197 -5.89007 -6.18092 -4.19083 -8.75869 -8.98044 -7.79407 -11.4465 -8.45284 -9.0068 -9.06136 -8.64976 -8.04639 -7.72256 -5.52254 -6.47254 -6.50068 -8.74209 -7.02282 -6.99811 -7.1144 -6.3062 -7.8887 -8.99894 -6.68959 -6.55602 -5.89352 -8.29815

ESB(Hz) 82.93247 98.05701 35.32976 11.34647 4.712815 15.51871 39.24576 59.61501 9.377832 34.80645 38.50865 3.631343 19.67833 9.887167 26.42553 13.95746 23.59405 17.7956 14.92859 13.91677 20.15103 74.24617 41.58923 23.63475 10.05151 21.55613 18.14172 8.838593 26.1694 41.9626 23.49122 7.237845

Pt 13.23812 37.17356 78.58236 45.46884 108.5139 16.05467 14.50952 20.22629 155.5366 90.11525 114.3295 102.1379 42.89559 60.95787 66.98698 76.71019 57.24394 107.6432 33.18504 84.55957 146.675 151.829 133.5169 55.53918 221.4947 161.8465 79.85773 82.91004 48.0308 54.50661 121.3556 66.33668

P60 3.294098 3.439334 20.21295 26.02064 66.54672 8.174649 5.223007 6.578393 115.9227 28.89872 8.740527 84.53294 26.4995 42.79653 21.94186 28.04462 20.39295 28.07782 12.33932 33.2033 41.35149 12.6383 20.7573 20.51862 151.1724 55.57544 25.86022 47.60458 12.27326 24.06373 39.47459 53.10634

P120 0.134261 0.404024 0.741935 0.247454 0.786963 0.10645 0.107284 0.208562 1.390064 0.653264 0.32227 0.325969 0.670841 0.748265 0.410105 0.565565 0.62916 1.098547 0.183875 0.634734 1.411647 0.722513 0.976805 0.30184 4.551039 1.610731 0.469624 0.404596 0.21716 0.647871 2.014878 0.372284

P180 1.085789 1.75525 1.272791 1.386491 1.517365 1.154821 1.288788 0.839188 1.562425 1.349944 1.473471 1.971037 1.507361 1.18778 3.655425 3.793736 3.040775 4.943573 3.144221 4.745297 6.555052 3.992549 4.579161 4.149628 13.80577 4.979248 4.79059 5.149418 1.940218 2.872131 3.592171 3.627744

P240 0.128726 0.209036 0.341353 0.194178 0.700928 0.134353 0.094217 0.423981 1.28547 0.262723 0.172831 0.281625 0.25195 0.307762 0.220115 0.236376 0.253619 0.738973 0.26738 0.607278 0.909425 0.311633 0.486411 0.304506 2.20927 1.053931 0.301366 0.310084 0.187362 0.568517 1.003718 0.433348

P300 0.155007 0.201141 0.291826 0.478316 0.945154 0.146386 0.10965 0.260929 0.599022 0.333754 0.176186 0.323701 0.295895 0.255298 0.184444 0.208813 0.179425 0.270474 0.341558 0.448722 0.620539 0.262258 0.382309 0.323109 1.931016 0.856456 0.323377 0.39865 0.155632 0.419615 0.603801 0.283433

P360 0.058056 0.095831 0.134831 0.092012 0.323151 0.073654 0.053895 0.178149 0.370288 0.088423 0.071658 0.136081 0.088479 0.107213 0.082254 0.107828 0.097617 0.117761 0.134365 0.276411 0.382525 0.121584 0.196077 0.176867 0.591794 0.476103 0.121658 0.150326 0.094962 0.18465 0.37781 0.190124

P420 0.092388 0.125823 0.104518 0.076805 0.293677 0.102364 0.072103 0.2775 0.102013 0.066733 0.081903 0.177038 0.115145 0.145983 0.159115 0.10951 0.201481 0.296713 0.349713 0.196803 1.526891 0.139826 0.177917 0.426434 0.3983 0.172739 0.157399 0.208057 0.169936 0.116515 0.272349 0.183895

P480 0.037518 0.058356 0.0727 0.044636 0.192546 0.04993 0.035842 0.05885 0.203149 0.047698 0.039585 0.076488 0.044603 0.070317 0.043112 0.058925 0.035134 0.089621 0.082308 0.123792 0.163071 0.071358 0.094294 0.097422 0.317567 0.214414 0.059298 0.075859 0.048622 0.081438 0.186514 0.13239

Palias 0.037053 0.063542 0.088884 0.059335 0.195799 0.050406 0.042825 0.079553 0.185283 0.066264 0.047886 0.078372 0.052903 0.071994 0.05618 0.076427 0.046893 0.112095 0.091064 0.154468 0.182031 0.079779 0.09902 0.096005 0.392426 0.224914 0.066558 0.094303 0.072041 0.098733 0.234942 0.131494


n 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

276

ID


Z ESB(Hz) 4.444459 9.182068 107.0249 24.66978 7.777417 31.965 10.49096 6.337143 20.50214 4.833638 9.338627 9.706264 11.99461 12.17708 6.921945 4.688157 7.082938 7.235844 5.969859 4.679795 40.68134

Pt 204.9383 333.0227 30.05838 90.80526 39.91568 103.8597 95.75628 39.11846 65.27964 42.35609 77.58392 76.0257 49.12072 51.67568 49.74667 72.93052 25.21473 29.11879 71.78243 127.5192 480.4507

P60 140.2923 131.9504 2.203825 30.07595 18.02398 31.57705 58.25458 25.96135 27.53479 32.00245 35.25382 42.63257 18.51651 26.38581 32.6616 57.42058 14.55318 18.11376 40.99952 93.78769 412.6636 85.89094

P120 1.640816 4.051211 0.217827 0.615295 0.158054 0.489939 0.385322 0.173757 0.502236 0.107308 0.393507 0.425594 0.233668 0.41285 0.102447 0.123247 0.095561 0.137466 0.136757 0.268494 1.255099 0.261234

P180 4.213022 5.133581 0.928222 2.205019 1.811689 1.92757 1.070242 0.930254 1.463432 1.43258 2.090408 2.34654 2.068701 2.300276 2.655465 2.470846 1.98229 2.297162 2.460339 3.174577 2.934094 0.610696

P240 1.059226 1.781259 0.189558 0.830048 0.207809 0.413513 0.186521 0.166465 0.370438 0.110639 0.543806 0.526892 0.27184 0.507186 0.069061 0.123142 0.060497 0.070765 0.06487 0.184576 0.630921 0.131319

P300 0.76736 1.115187 0.265871 1.098045 0.433576 0.538205 0.740444 0.342991 0.523951 0.374423 0.77311 0.77913 0.566435 0.895106 0.730361 0.90693 0.467435 0.680878 0.614095 1.067733 0.594303 0.123697

P360 0.362755 0.488893 0.092738 0.482471 0.108445 0.209523 0.097263 0.064905 0.135836 0.060968 0.292202 0.2797 0.128138 0.273576 0.035493 0.063942 0.031004 0.034057 0.036206 0.102099 0.320826 0.066776

P420 0.112908 0.09616 0.086833 0.168483 0.105009 0.151387 0.161568 0.071959 0.064687 0.076835 0.228909 0.143898 0.05459 0.19564 0.062709 0.076261 0.086752 0.201737 0.085851 0.186415 0.694303 0.144511

P480 0.166942 0.238335 0.049556 0.304965 0.050554 0.112234 0.056325 0.035714 0.081537 0.034444 0.155026 0.141246 0.057191 0.116588 0.020928 0.032089 0.012858 0.01607 0.021706 0.051989 0.362761 0.075504

Palias 0.187801 0.251207 0.056382 0.310273 0.051366 0.122955 0.077802 0.045386 0.081936 0.038508 0.186138 0.165226 0.071684 0.144281 0.030762 0.04672 0.024236 0.028966 0.033417 0.065945 0.260245 0.054167


277

n

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


Vcm WC(dB)

ESB(Hz)

Pt

-19.345

4.619478 2698.283 2109.298 122.347 22.66255 4.425396 20.81848 4.123352 12.53242 21.0625 14.91082

-13.9712 -12.4175 -24.0405 -10.6825 -12.1936 -13.1368 -18.7103 -19.4478 -12.8876 -16.1145 -23.7642 -7.15616 -9.46164 -8.34054 -10.2263 -25.9455 -12.1851 -24.8668 -16.4633 -29.7981 -9.56067 -34.5468 -34.7484 -5.70091 -24.8549 -11.4747

4.234382 4.123773 5.293148 4.121276 3.672305 3.07308 2.811842 2.659461 3.580831 2.674614 2.448923 7.653223 6.076691 6.798181 7.823617 2.418491 3.753182 2.642179 15.36767 2.496162 6.333313 2.409483 2.351729 14.71534 2.489807 6.730751

581.7218 581.6138 498.0644 444.4281 586.1344 5437.476 3397.068 6287.378 1689.227 14093.49 83659.67 1859.558 4855.675 4107.15 1074.347 61123.27 2069.249 31916.67 1952.598 194465.2 3979.638 379622.6 339117.6 1987.979 159321.3 8659.296

P60

446.2236 555.2468 431.4297 446.1711 790.8968 4590.605 3596.93 5621.647 2292.42 13702.46 87999.34 1331.197 3410.714 2955.024 1001.699 63356.7 2714.561 38482.63 1084.697 192681.4 2973.011 348722.4 375697.5 1097.117 165275.7 6853.931

P120

7.185935 18.52938 56.84058 36.78278 21.55114 64.71726 21.94413 47.09567 140.345 90.39315 135.617 199.0813 315.7535 340.6916 91.72725 55.22618 122.3756 337.69 196.1889 18.01582 291.8329 24.30878 35.7729 137.8405 131.738 496.9711

P180

12.10591 11.37349 20.19064 6.48638 9.595561 29.69784 26.07055 15.60701 45.49817 83.90869 90.58001 83.13667 177.1719 208.4305 76.16959 29.33841 157.1921 858.3225 227.0609 10.73721 63.03637 38.6095 34.19156 107.2181 25.96584 610.517

P240

6.903078 7.557654 7.244892 6.711089 8.838299 22.74687 15.97239 16.24003 51.0132 75.44471 45.38952 31.96153 198.1945 200.9331 68.84945 29.23984 20.78933 193.0638 61.99951 10.77226 128.2117 6.116021 9.096319 92.58808 93.35061 665.0395

P300

10.6105 12.3624 3.198654 3.738946 7.875399 29.26226 5.497064 9.117465 19.9935 83.81112 174.8084 64.55166 87.12716 69.24401 15.17263 13.00471 26.0785 70.16427 11.43279 149.85 112.0303 283.8125 257.3 70.95899 261.676 59.66039

P360

0.678913 1.669402 1.596861 2.032631 4.305943 13.60196 3.178508 2.277484 9.332641 14.39044 13.42763 20.04887 40.39604 32.65322 11.52444 9.478135 11.43586 39.13122 5.322254 6.824689 24.0387 3.453421 2.772926 27.97189 31.7063 59.12538

P420

4.791298 5.180988 3.37257 5.40969 4.59265 15.36706 9.720635 9.274561 11.85642 42.72648 89.45065 74.04457 23.75103 27.13706 20.92167 11.36167 50.86932 79.13692 90.07129 6.830576 115.8605 9.937331 10.66818 27.07853 245.8977 152.1391

P480

1.738181 3.232921 10.80655 8.813809 5.61883 21.73897 6.224648 15.37283 23.54016 30.18084 29.6918 34.03347 55.40925 57.89779 24.16024 18.83876 26.54462 38.26093 33.53121 8.8309 65.12831 5.108826 10.35594 28.07193 24.97705 80.80584

Palias

6.361254 10.12371 7.78848 8.961788 4.258873 16.08087 9.575983 14.30304 11.55876 32.75557 47.50076 88.2692 51.7575 51.99344 23.87876 20.3935 32.65996 129.4014 38.37783 41.75238 78.89239 33.6884 39.06768 48.13418 226.2061 86.31777


278

n

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64


WC(dB) -21.4101 -13.2457 -13.5418 -27.7744 -26.9404 -25.0497 -13.8532 -26.7022 -32.7482 -7.99116 -28.2471 -12.3296 -8.24374 -7.28129 -17.647 -24.0655 -25.33 -8.81938 -34.596 -10.936 -10.5079 -14.9072 -12.2771 -24.4845 -14.5924 -8.27297 -9.55242 -15.4835 -24.2615 -12.8105 -7.992 -11.5947

ESB(Hz) 4.423957 2.902734 3.243292 3.185393 3.216227 3.355734 2.671449 3.210368 2.531036 4.295587 2.645009 6.434721 10.6546 9.744908 8.09092 3.631222 3.701796 7.73388 2.682866 3.278926 3.507721 4.245767 4.174889 2.432955 2.817882 3.551449 3.277846 3.094741 4.275391 3.262768 19.12918 4.588406

Pt 8583.841 28347.67 8618.529 16722.59 17632.07 4854.913 43390.04 4201.153 2126925 10302.86 17312.71 4366.411 4565.376 6853.334 5345.708 5444.901 2446.025 3454.513 293305 2227.11 3456.937 10184.57 4749.538 371599.2 21408.04 22926 13356.93 12069.58 7756.635 11129.78 5565.063 1001.228

P60 11782.41 28176.39 9013.9 15511.25 12910.34 7031.246 38300.71 11786.05 1875321 10267.35 20350.23 3348.167 2435.715 4344.383 2854.542 5432.356 6928.749 2015.722 281239.4 2988.533 1471.343 6771.062 2334.822 334569.4 19624.56 19200.42 13653.59 11843.14 4452.966 7811.563 1407.847 46708.01

P120 372.685 194.9796 127.6877 492.4256 420.7472 259.1321 100.4263 111.1116 31743.2 635.9815 350.8097 215.3956 462.3099 621.8983 98.92325 250.8061 317.3844 64.2679 632.1662 34.62991 35.30338 19.96716 30.09699 103.5057 24.85653 63.08047 32.12665 4.087372 2.762062 17.9937 69.57457 165.7082

Vcm P180 P240 499.0603 491.99 452.3149 439.3512 319.8164 330.5887 915.1469 626.2664 339.1187 392.5521 358.7136 277.3549 313.8261 187.4231 1368.463 145.8274 12672.22 3423 210.5623 208.5527 190.9184 101.7909 240.4417 195.8835 339.124 418.5056 428.8511 511.5095 121.9935 113.2783 335.2948 344.8178 435.2786 465.0967 141.9436 68.67506 15251.66 30.67044 59.68456 40.09561 49.10827 31.20178 49.52358 28.05618 42.4329 32.12211 240.1025 48.13704 326.0583 80.63398 298.4861 127.8451 229.2062 61.62498 731.062 8.232185 1085.754 1.229578 586.9103 38.92185 467.0116 47.70656 8298.984 277.1897

P300 42.70219 98.56048 66.0912 52.04131 27.77274 21.45567 64.97735 56.75339 1623.677 92.13324 14.43616 74.03833 236.9087 368.9442 603.0074 80.06206 23.3841 25.0035 1264.917 18.08793 17.97459 12.67965 17.38503 1654.524 422.6227 188.4288 133.0447 238.4238 237.9959 216.4888 781.0811 1548.652

P360 23.1285 108.5463 71.58297 14.19162 1.263346 1.020662 77.82239 6.845821 919.4976 156.4734 69.03728 23.2753 61.37551 96.97794 7.285456 2.139296 28.81656 26.22356 111.0725 9.332499 23.19668 9.980889 17.7061 37.29144 43.34818 172.0658 46.12545 9.192325 1.037701 19.38736 42.92231 162.4121

P420 80.08452 125.2059 74.1839 62.69991 32.16684 24.49166 78.42698 58.50868 399.8098 154.3043 96.58591 101.3286 143.471 316.4065 533.5151 32.60233 79.26805 29.35307 1128.573 18.10099 19.4406 26.09363 30.96527 1689.196 254.9439 468.4554 232.7146 65.2677 176.3891 67.51479 802.1434 1135.399

P480 41.42974 69.92953 40.80157 39.37722 45.27581 36.09777 55.28798 54.83168 385.225 156.6186 86.25596 82.31367 166.2782 197.814 21.52648 50.78486 53.05748 29.81821 24.62913 10.96948 53.99992 11.43532 14.95059 34.42049 27.94532 267.0694 47.15474 11.60589 0.742147 16.76954 31.96421 78.06316

Palias 65.40513 39.10459 15.67155 32.41392 29.6943 21.70173 60.45474 44.78088 413.9787 71.28662 18.71557 124.2715 146.2418 209.0642 398.0267 51.03804 32.56595 17.76923 477.9267 10.1892 27.18242 12.57759 14.63973 652.2186 46.13293 296.3291 115.4977 267.792 115.6325 54.35798 685.0576 280.2492


n

ID


279

ESB(Hz) 3.054806 2.39401 2.840752 2.995774 2.484591 10.7924 8.363919 7.094901 2.889568 3.78677 12.65245 17.02903 15.96072 14.40094 74.5125 8.213549 6.082288 10.70741 3.283205 22.09644 28.54515 11.7387 13.93091 13.66788 24.52981 4.602481 6.515489 16.93641 7.635962 2.516097 7.797983 4.815813

Pt 2612.456 160545.6 5982.79 3831.816 39134.24 3363.736 1928.164 661.8248 1614.86 2310.954 1206.279 913.7911 2022.117 6328.986 2455.492 5609.689 1316.497 7416.066 665.1316 2168.479 958.2098 1406.357 1497.844 1338.411 1009.778 3976.184 2016.531 1056.885 1316.174 29767.63 1720.429 2226.594

P60 1213.133 197489 4712.113 3593.796 39769.94 1812.366 1327.341 792.6187 2498.288 761.1347 465.055 350.8137 710.9913 2279.949 359.0078 3586.495 804.5834 3459.679 844.9188 580.1383 259.7102 624.1786 584.5823 619.0563 110.8517 3432.104 1914.674 540.6985 899.5605 30714.1 716.8287 1131.018

P120 3.772485 64.89336 52.3793 62.32551 23.89858 537.2816 28.20556 12.31335 9.42399 19.02125 19.06046 22.28792 26.84742 25.1378 42.1297 127.7991 24.67354 117.2788 20.24997 48.8051 10.13563 12.28473 26.47818 25.65686 11.21487 102.5912 82.12531 34.93652 40.57342 35.02327 32.36812 18.19486

Vcm P180 P240 3.05495 4.587587 28.42348 8.012993 63.73363 73.15004 80.08443 85.48369 18.55889 34.41326 359.0153 429.3125 30.92813 46.382 19.29114 23.74208 8.406106 9.918059 30.98683 35.0052 37.54292 23.74145 24.05511 25.26804 32.52075 50.81066 37.39724 61.5894 65.11169 96.5735 150.1618 157.1378 29.96233 20.14345 172.4765 251.5965 20.62658 23.78753 46.69406 93.20233 60.50825 28.46256 26.77995 31.10931 33.37947 57.77572 33.53598 49.98685 205.7877 28.59319 85.16152 70.31911 77.79039 112.1555 52.12791 53.23908 32.51602 39.28774 73.81991 89.93684 56.1934 64.59391 53.5544 12.66139

P300 38.16917 54.33059 10.7364 10.00536 78.20227 86.05254 27.26981 15.29048 15.59416 20.13203 81.42974 68.02542 41.07071 46.37844 144.7842 168.663 50.7584 148.3074 10.76177 65.15417 91.09945 51.60592 37.37373 43.07012 124.8194 30.2274 52.13076 103.2187 23.70857 32.11819 35.66926 49.13533

P360 0.868307 4.351973 2.870735 3.50969 24.5406 76.79951 28.04606 14.41535 3.829371 23.14725 14.3866 19.36558 27.42031 48.12359 62.86287 84.68965 11.82721 100.1319 1.81626 40.88716 20.82014 23.81315 29.20405 30.40077 24.17257 30.46748 34.69632 36.43136 19.85864 25.58673 11.43382 14.08181

P420 31.2969 212.6373 89.39488 67.11564 209.4424 74.2494 27.47541 20.49986 4.939778 13.50537 62.59567 53.38948 46.71901 117.6829 267.9962 90.54524 31.78428 116.824 13.28382 34.67858 60.92133 34.78751 44.22698 38.5692 191.5782 73.53179 48.94611 52.08586 28.2445 80.94232 17.19052 14.16976

P480 1.003259 3.961447 9.599613 10.6396 25.04049 134.6912 22.14945 12.37611 2.125587 17.8902 15.51542 15.27636 27.48459 61.17971 53.02375 71.27672 10.09983 85.53009 4.018545 40.69208 18.70825 19.28329 15.25473 27.01479 16.26321 46.4098 38.52432 25.48388 21.46051 20.17116 10.9128 10.98245

Palias 4.222515 3.345564 7.759503 9.643766 29.42795 94.47458 22.57296 12.02786 2.34085 10.48131 24.05131 24.39513 30.73386 82.68812 67.16375 76.33151 15.86092 79.63006 3.863754 27.55483 25.95908 23.21416 30.57526 25.42217 44.17192 35.57935 31.95023 20.32935 22.28963 22.90321 17.65709 13.75447


280

n

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128


WC(dB) -2.77336 -5.52052 -3.14486 -11.765 -4.12983 -4.83909 -6.10665 -20.7875 -5.44926 -25.7481 -11.1981 -6.87445 -1.71535 -1.65016 -2.28685 -2.25325 -3.15974 -4.17116 -5.61498 -3.00604 -6.68522 -2.66674 -20.0888 -8.0629 -5.97106 -1.36524 -7.13197 -8.44442 -2.69864 -18.8599 -4.41515 -1.63558

ESB(Hz) 14.96546 5.015058 14.59261 3.041531 7.471045 7.384677 5.125583 2.985399 5.835569 3.273948 3.735409 4.770817 90.72847 81.08882 42.56254 61.32996 20.77724 19.26086 16.26928 25.65507 13.34727 27.549 4.944742 7.038487 7.556852 60.51733 7.149209 5.487005 18.49974 4.55549 8.272541 40.55298

Pt 988.3013 3476.133 2675.802 1742.232 3554.611 2323.963 2019.104 1854.375 2987.923 18832.42 3106.713 2361.531 1571.956 1727.052 2765.543 1510.652 1345.308 1623.858 1813.177 1362.164 1525.514 1331.905 2248.567 1964.041 2359.577 2467.373 1922.219 2042.348 1168.884 1150.404 1598.746 2774.666

P60 345.8303 1472.01 1073.519 1680.568 2161.302 1285.389 1495.951 1881.954 1977.986 14161.59 2546.826 1905.583 232.6713 233.2065 557.5984 229.159 487.1365 517.2598 593.1731 434.6936 606.9119 420.3756 1354.273 961.8603 1259.963 302.8538 939.922 1769.105 485.4436 1029.528 975.353 563.8199

P120 7.74568 18.3814 55.30033 13.87842 62.65187 20.59007 6.595251 2.31404 26.46354 27.18914 19.04343 42.76887 93.05877 80.23592 89.34977 69.49798 68.59512 61.14979 103.851 73.20179 95.38235 43.37584 14.25467 13.61319 20.31761 55.17945 16.39299 19.03333 42.10623 4.343844 29.61991 87.49939

Vcm P180 P240 18.37302 21.88636 37.3499 37.93444 25.59075 75.63627 18.38349 20.8482 66.46158 103.6925 35.97274 53.12359 29.72479 23.12555 52.44317 3.45064 52.1564 29.8089 125.9888 47.86579 125.9136 30.80763 84.13365 81.17053 98.73652 116.5548 116.4671 107.8987 147.9459 163.854 109.3646 128.0414 105.6199 103.8769 125.791 106.1124 435.5936 137.7315 115.8473 85.00535 264.6939 127.2432 92.63417 78.10702 331.7934 14.25796 248.8543 19.33948 244.7127 37.12444 70.6149 48.47588 217.0831 26.94421 263.3791 35.30372 29.06827 46.05136 210.7035 4.633275 75.8458 28.2754 76.20604 103.7392

P300 36.78489 58.27986 59.06946 6.734355 75.7456 37.64347 38.05693 40.86466 63.32891 748.6941 51.71835 29.74906 50.65357 47.234 48.92193 51.55398 51.34773 78.14351 103.7425 21.58522 56.90356 30.15935 177.2596 163.9088 156.8833 52.12298 142.7689 261.8022 41.27967 165.6092 85.90505 93.10697

P360 19.51138 24.60272 41.34536 4.904569 51.90959 34.58501 21.39923 0.606409 27.07595 6.228798 10.45475 18.00933 38.68284 40.62593 79.54715 35.75476 37.87019 40.17457 17.06333 22.40112 15.80568 30.40511 0.710476 10.35845 26.1304 38.7266 13.26117 16.79866 22.82791 0.557273 24.85145 56.18003

P420 24.19422 26.08977 51.11187 9.909967 82.38267 30.21903 35.68231 30.44575 72.63219 1097.846 180.5229 74.41163 40.42417 38.56704 59.70375 34.5724 68.21219 68.55239 91.32923 46.28685 164.4151 49.29064 77.90416 82.51806 100.0346 43.27688 67.62393 47.08927 24.63412 5.770889 28.46965 47.20738

P480 19.27182 22.74711 51.11349 5.727201 47.80459 23.36171 19.84904 0.637749 31.8547 6.113371 11.08823 17.61549 31.40534 34.70553 40.39908 29.34701 40.4535 44.61057 21.20231 28.92012 18.42621 25.32356 1.066137 9.595389 25.48426 35.25919 11.96163 15.57911 25.41298 0.621054 24.0471 39.72095

Palias 25.07533 24.3027 28.41966 4.283409 35.25934 23.07722 17.72572 0.608828 26.22132 229.1407 9.133733 17.35606 42.00987 36.25599 58.11509 27.36437 38.90885 42.23115 43.33246 26.2012 21.06245 23.43402 15.16835 25.25884 34.18773 33.57544 19.69459 28.70025 21.47349 10.41716 25.2576 41.96903


n 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

281

ID


ESB(Hz) 5.098561 7.858679 3.469834 5.186012 4.375129 4.17809 22.62673 5.855952 5.738436 5.483044 17.04975 33.50025 6.806942 6.837763 8.957319 5.95808 6.690761 7.238107 6.788575 7.098731 10.52156

Pt 2262.656 1112.643 2569.09 3657.612 895.9433 820.2995 1568.026 2623.268 2684.739 2462.273 850.5481 1137.025 3049.771 2755.336 1753.02 2280.799 2277.696 2098.801 1939.975 2110.605 38717.82

P60 1284.217 669.6974 331.8579 788.3503 619.2135 630.3706 439.8496 1515.527 1452.886 1501.498 368.1943 308.9879 1662.117 1580.185 1019.096 1301.329 1238.229 1224.781 1210.109 1195.47 36357.21 93.90303

P120 9.258033 10.5703 19.79994 38.16017 35.58189 33.61368 27.45218 59.85719 40.43145 41.30634 33.00151 38.45049 113.0813 120.6547 62.78877 83.82175 77.73569 68.94843 78.86849 76.21673 360.8564 0.932016

Vcm P180 P240 169.9129 22.7359 143.9072 25.11255 32.92985 39.22593 60.88035 77.72693 55.38725 52.7668 50.2438 46.47928 42.13817 49.93908 87.18929 92.82229 64.8472 78.47066 76.07 72.24766 32.2173 23.83999 27.45009 24.88588 189.1934 181.7846 168.9123 168.4655 93.02595 98.5999 104.6726 100.105 97.51813 117.6 87.28168 99.3157 93.49989 117.7128 95.71242 115.5192 457.6894 128.5279 1.182116 0.331961

P300 163.8245 104.4849 29.74868 53.7124 14.36949 12.12198 35.98089 42.17919 51.01479 40.95956 21.73613 39.00293 47.48853 48.77145 31.0827 38.6268 50.86113 42.74097 32.85949 52.15289 140.3556 0.362509

P360 9.74151 13.28834 19.786 38.18324 0.937234 0.914813 27.39489 19.43655 28.99183 23.08497 19.3017 27.85645 27.35562 21.20576 14.00661 21.83421 23.80233 18.55993 20.76524 19.53976 36.54063 0.094377

P420 17.73617 12.12087 22.60372 40.56567 5.657186 4.917534 28.67487 26.05344 29.01968 23.22101 25.23201 24.41861 47.1156 33.32256 24.24466 23.02306 26.44533 23.63644 26.36373 19.33985 120.0638 0.3101

P480 8.099284 9.099957 21.44912 37.33584 3.390236 3.077888 25.49081 18.80064 20.18161 20.84905 21.80389 23.1329 23.24885 23.42048 22.78454 14.07575 23.61658 21.68005 15.00078 19.31527 37.07491 0.095757

Palias 11.3831 13.84505 20.46559 33.25088 3.097451 2.870695 28.50238 19.14618 18.1983 15.96142 14.86008 22.52719 17.65486 22.47604 25.05034 18.73053 22.40467 21.03967 25.91783 23.52342 64.77355 0.167296


282

fn

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


WC(dB) -9.13582 -5.48064 -6.77833 -8.04621 -8.98095 -7.97297 -4.13505 -5.17429 -6.57122 -7.15604 -2.54187 -2.68266 -3.72138 -3.30208 -4.45507 -3.53927 -7.44935 -3.9535 -4.23972 -4.22978 -4.4173 -3.60728 -3.12456 -6.84864 -5.08624 -3.01068 -4.19039 -4.69865 -5.79529 -7.13278 -7.68242 -5.04393

ESB(Hz) 71.67137 178.7716 106.1265 85.13922 52.42792 50.28685 104.4724 61.44877 60.56001 49.84596 132.8015 141.1841 129.3498 123.0909 110.4096 111.2551 60.44442 113.768 115.7663 135.1923 105.1948 106.9183 140.6605 26.3529 39.45783 131.1872 108.2869 88.11617 70.24965 30.72175 50.20166 86.76047

Pt 12.29049 172.7253 48.5286 88.56369 24.47172 41.67723 21.18508 16.9082 29.93175 101.7775 81.29038 22.36013 13.59194 32.82244 122.9164 145.4998 50.59537 29.68 71.65134 106.6232 37.22974 1.02395 21.32749 31.94493 15.04237 943.8032 76.0372 10.50067 15.30454 39.93408 65.25423 18.08254

P60 2.112406 2.64E-05 4.984697 3.713033 8.726198 10.96258 1.257548 1.49131 2.228995 9.240596 3.853513 1.263396 0.695098 1.553757 6.684792 12.09901 3.258438 2.994965 5.449548 9.63289 3.305147 0.037471 2.06783 9.603149 4.43101 118.1728 7.041963 0.54918 0.749836 16.92979 1.783511 1.678684

P120 0.212137 2.05E-05 0.938572 0.917879 0.42497 0.465092 0.296093 0.225655 0.268985 0.540905 2.135488 0.556454 0.158196 0.377777 2.590919 2.220778 0.491949 0.469666 1.112823 1.345061 0.4707 0.01502 0.400881 0.351876 0.16422 29.08081 1.402981 0.154962 0.1815 0.233344 0.270087 0.192509

X P180 P240 0.418882 0.071314 3.23E-06 2.89E-06 0.917332 0.944746 0.886559 0.413072 0.495765 0.203572 0.783223 0.3497 0.848963 0.328473 0.595389 0.140436 0.828978 0.195969 1.130919 0.719348 1.89012 2.784942 1.99518 0.720389 1.627085 0.166851 1.152588 0.429891 2.484383 1.548551 3.674845 2.549955 0.540551 0.273065 0.473851 0.423593 1.586065 0.960568 1.60774 1.394709 1.377639 0.570151 0.242827 0.020295 0.469924 0.452971 0.268737 0.147704 1.258347 0.128383 17.88422 33.57747 2.146012 1.430844 0.172014 0.12083 0.17797 0.13672 1.090709 0.161951 1.134988 0.27449 1.103287 0.170722

P300 0.049871 3.02E-06 0.368843 0.245869 0.111363 0.216736 0.219278 0.157133 0.150217 0.487034 2.036851 0.435037 0.299886 0.703279 1.278228 1.772625 0.234192 0.213964 2.170166 7.555363 0.385678 0.026752 0.262855 0.258006 0.294491 25.07542 1.022966 0.086165 0.097641 0.206448 0.205389 0.119581

P360 0.016578 1.26E-06 0.132965 0.261509 0.048537 0.085265 0.238985 0.130253 0.178574 0.287832 1.959061 0.602302 0.199372 0.486913 0.854605 0.914234 0.183382 0.188479 0.556725 0.586996 0.22698 0.012881 0.160319 0.095955 0.078197 15.08111 0.778345 0.090114 0.087913 0.107031 0.162347 0.147319

P420 0.013964 3.23E-07 0.048741 0.087592 0.017413 0.029284 0.149295 0.059291 0.093757 0.19832 1.311995 0.366293 0.125171 0.198581 0.401803 0.545547 0.097096 0.200809 0.726904 2.544955 0.200776 0.010075 0.187413 0.062881 0.058803 11.59501 0.544279 0.063665 0.074447 0.076333 0.090674 0.086733

P480 0.004975 3.52E-07 0.022898 0.023604 0.012283 0.018585 0.107483 0.052187 0.059489 0.182711 1.133474 0.320083 0.080944 0.177124 0.359876 0.389867 0.055723 0.231991 0.183431 0.274334 0.110397 0.006639 0.108855 0.043438 0.043472 7.4541 0.41198 0.04664 0.043191 0.067074 0.06756 0.068815

Palias 0.005712 4.22E-07 0.033025 0.027027 0.013085 0.020069 0.129219 0.074601 0.094785 0.15867 0.859749 0.283093 0.104264 0.215752 0.295792 0.435142 0.089505 0.364067 0.17775 0.360024 0.135768 0.010927 0.173561 0.051648 0.084229 7.822257 0.360953 0.05169 0.051212 0.083497 0.075413 0.084134

Appendix E. Noise characterisation of filtered data

283

fn

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64


WC(dB) -3.81046 -6.11902 -2.91217 -3.43452 -4.68414 -3.83315 -4.63035 -4.00368 -2.75985 -4.8797 -3.36342 -4.37236 -2.58574 -3.48857 -5.03184 -6.96265 -4.40453 -2.08494 -5.58583 -4.44802 -5.87892 -2.66468 -3.47157 -3.56228 -7.42318 -3.9462 -3.70127 -4.63932 -3.84524 -4.84429 -7.00496 -7.64086

ESB(Hz) 141.8392 65.35311 153.4125 123.1197 106.8554 98.22035 76.14019 134.4231 142.8076 84.11056 137.8493 108.7183 158.555 80.31631 55.54611 85.65373 129.9217 218.4557 73.73931 104.6858 56.30644 153.3272 177.0403 90.19299 38.8457 123.0209 93.64234 88.75647 103.0206 86.15032 67.8765 86.37294

Pt 27.93151 103.5104 59.8012 20.60933 19.85111 19.30832 12.7545 124.2561 11.00275 55.11124 4.312444 57.87931 27.85124 20.81541 202.8561 197.2327 66.98364 18.02236 26.63843 19.92159 473.9456 49.24353 160.0513 64.54178 400.6169 18.37642 9.036208 19.33837 9.876069 12.86993 30.66546 107.1466

P60 2.366453 3.806242 2.009754 0.809723 0.991077 0.786076 0.446033 8.966944 0.472492 2.267281 0.227651 3.34197 1.522992 6.106761 80.52308 15.6307 10.58124 0.775728 3.6025 1.808645 48.40693 2.764131 4.98403 14.79656 154.8595 1.368577 0.462594 1.796379 0.687799 0.859305 1.977685 9.3602

P120 0.533807 1.01 1.234612 0.326808 0.171643 0.19278 0.138227 2.829834 0.147929 0.478713 0.039686 0.976186 0.40008 0.411908 2.271496 1.935045 2.025337 0.387224 0.240595 0.243921 2.094049 1.317547 2.848208 1.227393 2.475398 0.369467 0.115804 0.387362 0.182447 0.178228 0.395093 0.720224

X P180 P240 3.441293 0.447799 1.130961 0.920029 1.878872 1.513311 0.892292 0.373906 1.777151 0.244712 0.496001 0.265546 0.315138 0.163286 2.064865 2.593736 0.200845 0.230636 3.843498 0.626686 0.614523 0.071338 2.01649 1.553877 0.747501 1.10539 0.643921 1.043256 1.453438 10.43975 4.070342 1.317284 4.74731 2.34256 0.81712 0.573385 0.126265 0.175911 1.047588 0.204986 2.503391 1.967357 1.526682 1.189376 4.881697 2.979234 0.942059 1.691701 3.998172 5.432391 0.431304 0.277684 0.167093 0.134416 0.308234 0.250717 0.16055 0.135446 0.214999 0.142048 4.314977 0.278624 0.709761 0.305681

P300 0.520833 0.514126 0.807188 0.283691 0.240203 0.165258 0.116883 1.491349 0.26923 0.506766 0.091665 0.508381 0.338208 0.225858 1.321821 0.75142 1.164669 0.426736 0.098301 0.165275 1.112179 0.908472 7.60274 1.389327 5.519626 0.219296 0.097545 0.176138 0.095226 0.129517 0.447335 0.288465

P360 0.24837 0.386125 0.619917 0.226924 0.171917 0.185241 0.106576 1.062415 0.153586 0.285559 0.058585 0.245315 0.20038 0.138802 1.155112 0.572003 0.576354 0.265653 0.189103 0.156211 2.078966 0.524137 9.853621 0.729688 2.454909 0.157915 0.079571 0.184207 0.076761 0.093255 0.224709 0.16099

P420 0.166111 0.286561 0.328814 0.142492 0.074504 0.075272 0.065009 0.515718 0.093941 0.177939 0.038358 0.507815 0.252644 0.289321 29.62208 0.364985 0.482102 0.130054 0.267107 0.085281 9.051268 0.608586 11.38451 0.464521 2.883638 0.190847 0.175024 0.134063 0.128911 0.078465 0.297593 0.402696

P480 0.105167 0.174907 0.223659 0.09202 0.045833 0.051707 0.05656 0.436355 0.073547 0.128774 0.02759 0.581661 0.220305 0.230941 3.072133 0.264084 0.421271 0.086454 0.076761 0.055551 24.4744 0.490023 3.226394 0.424486 2.549643 0.060948 0.048784 0.080157 0.045526 0.058801 0.181921 0.086063

Palias 0.112211 0.210774 0.251571 0.133648 0.082402 0.08546 0.084483 0.473528 0.090426 0.167408 0.04097 0.937687 0.187881 0.159577 16.92952 0.330245 0.377412 0.112845 0.151096 0.106175 21.66914 0.961182 1.56835 0.54606 2.570648 0.122037 0.083058 0.110164 0.057318 0.084801 0.183249 0.123153


fn

ID


284

ESB(Hz) 96.3914 73.66015 110.4784 173.0386 78.80764 14.11396 98.90578 115.7007 116.337 111.99 107.5678 97.91904 59.35326 114.556 53.34933 101.2086 46.77173 126.6125 214.3714 58.5038 136.2381 82.2719 175.7435 86.01652 90.96971 83.4794 66.15898 130.8823 78.20315 70.50546 71.88657 155.4387

Pt 44.87779 39.94036 107.7856 34.7778 12.52272 41.86027 32.50596 20.16167 14.37471 51.42489 15.28369 17.60683 32.18745 15.58732 12.06756 17.9765 21.23449 50.92393 79.43515 14.21526 10.1261 44.85382 39.9187 49.36509 147.8253 20.28966 46.69568 69.87584 28.08203 45.62914 55.15863 6.651967

P60 1.48059 1.486976 7.759335 3.802328 0.513302 22.26551 3.526986 1.317668 1.623701 6.335079 3.335566 3.315265 7.512004 1.488117 5.603682 2.730478 8.672851 1.657053 4.305345 3.639923 0.938374 1.251255 1.70843 4.086568 11.98671 1.250872 2.985935 12.90461 1.608782 1.725352 1.985127 0.272251

P120 0.452433 0.373022 1.335348 0.67864 0.13999 0.289093 0.384781 0.281854 0.194359 0.87002 0.223328 0.200035 0.217509 0.137234 0.107007 0.189821 0.165809 0.524173 1.938657 0.089945 0.21166 0.263164 0.934654 0.437831 2.144674 0.137889 0.481328 2.224026 0.275709 0.388203 0.457055 0.088971

X P180 P240 1.393392 0.474067 0.261522 0.379297 2.577894 1.133926 3.730764 1.029955 0.636355 0.14426 1.31738 0.279325 1.575615 0.348438 1.415258 0.299796 1.703893 0.124692 1.977408 0.659925 0.243378 0.305112 0.72134 0.219017 3.250456 0.221245 1.823099 0.146878 1.381285 0.094522 1.32746 0.126572 0.299516 0.150976 2.788889 0.469655 3.555271 1.888893 1.519506 0.099035 0.226381 0.189933 0.871339 0.223023 1.086389 0.999824 1.466671 0.314831 0.975565 1.09256 1.27158 0.126207 2.410955 0.238001 1.895885 1.015445 1.838468 0.204921 2.408427 0.325518 2.601669 0.414249 0.155943 0.111481

P300 0.378232 0.274027 1.137972 1.024396 0.094926 0.294375 0.596379 0.482665 0.119517 1.174247 0.293465 0.22929 0.430004 0.128138 0.069895 0.077139 0.069788 0.254788 1.22266 0.143146 0.123387 0.166904 0.758691 0.198257 0.807402 0.146716 0.238675 0.550669 0.168599 0.275781 0.310319 0.072015

P360 0.280185 0.254177 0.705503 0.568568 0.093463 0.158865 0.152281 0.149598 0.100897 0.343527 0.227549 0.215447 0.125523 0.099814 0.103672 0.084439 0.103463 0.168868 0.690804 0.107345 0.110175 0.138304 0.458118 0.166996 0.525789 0.095849 0.150738 0.352062 0.113824 0.253436 0.276152 0.076411

P420 0.223134 0.13867 0.815222 0.49214 0.283398 0.208298 0.132442 0.172955 1.415007 0.306418 0.308731 0.237979 0.094669 0.044824 0.04779 0.067375 0.068344 0.10009 0.359864 0.046721 0.060859 0.071939 0.286072 0.097275 0.295302 0.057735 0.090619 0.189864 0.062924 0.145953 0.175891 0.03939

P480 0.116102 0.110545 0.300775 0.357785 0.056835 0.083736 0.071295 0.072284 0.051125 0.184513 0.178197 0.211825 0.045363 0.032338 0.036223 0.038266 0.039968 0.083824 0.252228 0.03678 0.047755 0.050416 0.212879 0.074759 0.232334 0.033898 0.07104 0.149033 0.048538 0.134466 0.130042 0.026643

Palias 1.58E-01 0.138259 0.424672 0.317919 0.224205 0.121371 0.098854 0.236012 0.147747 0.199039 0.169005 0.210103 0.054789 0.064566 0.090609 0.05732 0.084239 0.127193 0.278652 0.076218 0.090436 0.078601 0.240659 0.107981 0.231656 0.062827 0.105647 0.15324 0.063993 0.126045 0.137441 0.060449


285

fn

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128


WC(dB) -3.14022 -3.15547 -4.14199 -4.1409 -4.81759 -3.76173 -3.64143 -2.52779 -3.44162 -4.89954 -4.8431 -3.51353 -8.12103 -5.94625 -5.39706 -6.70861 -5.4559 -6.07432 -2.8873 -4.77216 -5.15871 -5.56365 -6.14384 -4.28356 -4.25619 -5.52569 -4.07979 -4.12971 -2.94305 -4.78114 -3.95064 -3.71586

ESB(Hz) 123.4877 135.8383 108.9142 110.8391 92.6791 132.35 123.747 231.7375 131.6764 101.5964 86.92567 106.1739 12.80544 41.27909 74.55295 67.80372 89.0213 90.97248 144.6197 72.14069 51.57453 90.86894 79.06396 90.55209 84.43523 74.79964 107.4603 131.4368 161.4318 84.09487 115.78 90.15922

Pt 13.42336 9.403102 27.80735 23.85343 132.3348 24.83992 5.210132 46.21064 26.95263 26.84236 15.91884 24.45349 67.78584 43.60379 38.9572 42.72048 84.52871 108.6989 74.62742 39.0457 72.55379 39.3526 169.3509 87.10463 74.30311 58.04636 64.64078 36.36293 27.00784 13.75596 57.50622 65.3557

P60 2.169465 1.321764 1.266475 1.040337 5.507222 1.0634 0.376777 1.797551 1.191611 1.034075 0.752066 1.353683 33.19704 15.79535 8.371978 7.306758 11.49813 14.02649 3.86355 7.711166 21.47955 3.783796 3.501176 11.65684 3.30689 3.357787 1.517213 3.177774 0.841765 1.153277 2.580098 3.266213

P120 0.389778 0.130263 0.317247 0.304685 1.688414 0.420308 0.104396 1.596227 0.413795 0.336839 0.111715 0.296153 0.31844 0.361246 0.388254 0.34122 0.79308 1.964335 0.800087 0.412377 0.879536 0.315758 0.654596 1.095742 1.097287 0.479405 0.522812 0.724154 0.401651 0.236514 1.062807 0.294352

X P180 P240 0.311764 0.40892 0.452274 0.202992 1.360807 0.293597 1.419164 0.263255 1.934733 1.676902 0.665347 0.316999 0.609593 0.101726 1.135995 1.61348 0.528901 0.401414 1.34519 0.30664 0.445215 0.125708 2.974817 0.361389 1.31501 0.301579 0.965649 0.369804 2.218816 0.348679 2.610778 0.330714 2.00446 0.665401 3.000745 1.687928 1.424571 1.215415 1.833132 0.449472 0.813763 1.148778 1.231609 0.245886 0.50559 0.614327 1.727774 1.361101 0.967721 1.549597 0.772927 0.427978 0.539917 0.565121 0.71424 0.752773 1.786452 0.526138 0.190825 0.177404 0.883217 1.097461 0.914015 0.443123

P300 0.212799 0.146064 0.234506 0.24063 1.063071 0.195231 0.103025 1.06804 0.248357 0.149245 0.113661 0.365611 0.508437 0.479419 0.604245 0.410025 0.608379 1.064282 0.728006 0.751822 0.90289 0.490343 0.324152 1.523168 0.96367 0.350539 0.341595 0.507172 0.408423 0.116878 0.679888 0.275174

P360 0.152802 0.102781 0.18554 0.15431 0.614725 0.131256 0.077799 0.582834 0.185379 0.113973 0.084443 0.197495 0.14358 0.176219 0.153798 0.130451 0.225695 0.508003 0.488466 0.203266 0.269015 0.151449 0.226846 0.587158 0.615529 0.19218 0.241466 0.236842 0.209668 0.074355 0.421629 0.189614

P420 0.095526 0.053258 0.12855 0.076712 0.314978 0.081608 0.061411 0.22553 0.104655 0.065328 0.07904 0.123368 0.13167 0.163252 0.147971 0.10456 0.204352 0.340339 0.26508 0.175903 1.451577 0.144286 0.167146 0.57945 0.414105 0.181664 0.14915 0.172338 0.138982 0.084471 0.273574 0.184311

P480 0.064503 0.040999 0.082615 0.050658 0.24353 0.040824 0.029756 0.159798 0.072006 0.040194 0.044027 0.093359 0.059837 0.084277 0.074387 0.045202 0.113338 0.237619 0.173056 0.081575 0.171558 0.103073 0.103676 0.362995 0.217368 0.093923 0.086932 0.101038 0.101701 0.040495 0.157017 0.090887

Palias 0.12531 0.081717 0.086488 0.081026 0.258728 0.071087 0.047499 0.170877 0.081761 0.061364 0.047267 0.122878 0.092614 0.095695 0.089702 0.06494 0.109334 0.252777 0.202035 0.100335 0.168076 0.079013 0.121593 0.333236 0.233066 0.090499 0.091059 0.099518 0.104864 0.043109 0.158264 0.105959


fn 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

286

ID


ESB(Hz) 97.43331 82.66571 101.5884 80.2565 144.7402 157.5559 74.83024 137.3292 80.75387 114.945 120.249 104.3316 150.6273 140.4463 85.28961 109.5105 69.00759 73.91522 42.27614 70.44276 100.4502

Pt 12.59104 18.52842 82.46384 89.61593 17.66598 16.55165 60.34342 11.73879 32.15311 19.36701 32.3015 28.57497 19.61727 46.71735 20.46267 13.96998 23.91663 23.80127 16.58218 63.14817 60.92485

P60 0.80409 1.09987 4.113528 3.863173 1.836327 2.561402 3.998839 1.227244 1.524871 1.68006 1.554815 1.382765 1.370467 5.70001 1.692286 2.501096 0.88214 1.248523 2.263368 2.877145 7.473391 12.26657

P120 0.18276 0.204615 0.460709 0.831194 0.232666 0.277042 0.69143 0.225649 0.214686 0.232657 0.574245 0.507718 0.230305 0.880724 0.170381 0.147968 0.156571 0.169815 0.084787 0.488294 0.877905 1.440965

X P180 P240 0.16976 0.164571 0.179573 0.166245 2.686396 0.30575 3.509625 0.73078 2.025199 0.333932 1.232901 0.422014 1.477437 0.258926 1.006395 0.201434 2.888327 0.143716 1.735006 0.206236 2.206709 0.740135 1.661351 0.428355 1.578996 0.190821 3.212478 1.011447 3.171011 0.12212 1.413843 0.141637 3.295649 0.067785 4.059105 0.105708 3.669096 0.063306 3.146713 0.255347 1.505683 0.985826 2.471378 1.618102

P300 0.117076 0.153597 0.2383 0.484184 0.255708 0.382666 0.19777 0.135602 0.101907 0.174603 0.582573 0.287759 0.191187 0.759112 0.140998 0.182438 0.139327 0.245814 0.129855 0.162654 0.801158 1.314993

P360 0.083274 0.103561 0.133687 0.272729 0.146227 0.216527 0.116985 0.087267 0.090754 0.10618 0.403241 0.195059 0.09587 0.406642 0.076956 0.070448 0.063162 0.071045 0.04995 0.124006 0.497114 0.815945

P420 0.094672 0.083976 0.088769 0.177458 0.109072 0.136855 0.158378 0.069281 0.074273 0.074747 0.26443 0.166466 0.053167 0.189582 0.057499 0.073596 0.091457 0.199766 0.080553 0.181967 0.729852 1.197954

P480 0.050021 0.041231 0.059737 0.124098 0.062287 0.091582 0.055787 0.033347 0.032088 0.047198 0.183888 0.089438 0.033691 0.158077 0.026984 0.023602 0.021904 0.024139 0.023128 0.050616 0.444959 0.730341

Palias 0.054016 0.061511 0.073689 0.135519 0.078518 0.086282 0.075285 0.060519 0.071899 0.065628 0.18252 0.090239 0.053252 0.117315 0.052129 0.047081 0.039893 0.046648 0.057317 0.136174 0.546466 0.896952


287

fn

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


WC(dB) -9.0162 -5.96083 -9.57099 -9.38975 -6.51691 -8.04842 -4.68401 -8.03771 -4.06984 -10.5653 -2.99456 -3.00473 -4.73832 -3.40694 -5.33054 -3.211 -6.06463 -4.67346 -3.88508 -4.15723 -5.11825 -4.14369 -3.70486 -5.32848 -8.05014 -4.19413 -4.23534 -4.53237 -6.33093 -7.58308 -4.02462 -3.64067

ESB(Hz) 25.01328 56.03957 80.35674 76.607 104.3321 36.87059 88.85975 19.80753 107.4046 16.9641 130.8941 119.6023 139.65 172.9932 106.8984 116.3166 52.1828 113.677 148.0338 141.3794 108.6967 148.8697 126.6498 56.90896 33.46487 119.5496 136.2828 126.9489 65.50478 21.95981 105.1668 161.4714

Pt 8.407443 93.60097 144.989 159.0144 40.72735 108.9732 16.71338 60.20401 23.51897 99.366 18.60576 9.489305 26.93678 38.07913 102.6979 98.89952 22.58289 27.00405 51.55167 60.04019 29.23298 8.409426 9.79271 17.45217 184.225 165.8704 37.85822 18.23994 60.86633 33.6556 62.81003 6.405274

P60 5.398421 4.640978 16.51336 10.34474 3.371395 33.29122 0.519504 1.88135 2.129552 66.57373 0.8834 0.458435 1.671759 2.5914 5.954355 4.166873 0.879573 3.20837 4.58758 5.984533 4.153058 0.420601 0.553919 0.812549 79.98419 14.6952 8.09407 2.197389 8.141108 21.03283 2.473522 0.468154

P120 0.352082 1.176537 2.040813 1.911117 0.791962 25.03357 0.204388 0.436115 0.401006 0.546197 0.393475 0.186184 0.361755 1.00784 1.520312 1.271957 0.220411 0.56485 0.959675 1.505426 0.462468 0.183778 0.234284 0.355086 1.27814 6.474369 1.16287 1.540684 1.940279 0.348549 0.551931 0.145639

Y P180 P240 0.68736 0.091312 0.512711 0.907899 2.140836 0.994483 2.003153 0.532682 0.536176 0.293057 2.806875 0.708375 0.861661 0.218528 0.499689 0.428825 1.240451 0.372973 0.762441 0.332345 0.635754 0.487798 1.137264 0.293084 1.57472 0.303421 1.423276 0.552935 2.413939 0.778073 2.700363 1.923315 0.60859 0.243118 0.505221 0.350798 0.923222 0.688765 1.159896 0.640102 1.186045 0.283687 1.018108 0.131403 0.355969 0.231019 0.305294 0.190425 2.002205 1.226063 4.05749 2.779533 2.194683 0.870239 0.279468 0.247116 0.497399 0.243302 1.0514 0.247554 2.571154 0.639828 0.795174 0.132476

P300 0.051935 0.542202 0.333802 0.234264 0.3297 0.290129 0.117514 0.189338 0.209552 0.221494 0.365065 0.156102 0.209062 0.594081 0.478427 1.622737 0.178622 0.190934 0.482144 0.576136 0.220056 0.135705 0.132971 0.216874 0.532311 2.216728 0.464606 0.201725 0.334498 0.157262 0.497366 0.285797

P360 0.016137 0.359237 0.121056 0.161275 0.113006 0.196015 0.102446 0.237085 0.166265 0.111954 0.348737 0.193868 0.123479 0.308201 0.312173 0.915503 0.10328 0.131781 0.240302 0.269879 0.148389 0.053624 0.055309 0.062259 0.334079 1.476294 0.323292 0.131786 0.124681 0.085397 0.372723 0.046313

P420 0.01154 0.261991 0.06922 0.080581 0.080605 0.150557 0.09847 0.11694 0.153452 0.123414 0.283233 0.135074 0.087288 0.15598 0.22426 0.503365 0.078502 0.074805 0.221086 0.209163 0.099543 0.040291 0.041791 0.05081 0.234147 1.065646 0.285217 0.085408 0.067264 0.057989 0.237877 0.029587

P480 0.003689 0.169736 0.055433 0.043922 0.056969 0.116398 0.054591 0.189687 0.092182 0.153785 0.220512 0.116591 0.076326 0.128577 0.140114 0.349893 0.070389 0.054289 0.157674 0.164082 0.078067 0.027622 0.025813 0.042653 0.225725 0.62748 0.146966 0.041363 0.054553 0.044833 0.175331 0.035139

Palias 0.00459 0.225589 0.056416 0.044012 0.063162 0.174003 0.100615 0.160984 0.113325 0.135119 0.20763 0.107367 0.080102 0.133401 0.183389 0.462257 0.076548 0.074001 0.145051 0.156243 0.113653 0.038548 0.045582 0.051296 0.23535 0.610305 0.13724 0.091718 0.093236 0.066733 0.188625 0.066352


288

fn

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64


WC(dB) -4.60713 -5.87509 -6.37083 -3.10174 -5.66907 -4.167 -2.89788 -4.45477 -4.10524 -4.40558 -3.68099 -7.81281 -5.35557 -3.1748 -5.31174 -3.05486 -4.79189 -4.02794 -4.69778 -3.87431 -5.75188 -3.91947 -4.39332 -4.68134 -2.51348 -4.21839 -3.40726 -5.94453 -5.78554 -5.25625 -5.01214 -5.77805

ESB(Hz) 86.61129 94.41924 93.11667 148.0381 117.2395 125.1717 145.8354 128.0404 112.2467 126.1922 127.4626 77.22192 103.0646 154.688 89.17095 160.1631 127.1832 139.1861 57.79569 184.8045 95.26056 123.796 93.20129 50.48459 215.5278 113.4019 110.1041 87.52462 84.10863 96.77111 98.62637 44.8154

Pt 43.80987 102.7212 150.0456 11.32869 41.12931 5.552178 7.44625 149.0752 18.32689 77.04694 5.213638 94.78587 35.40231 16.13216 37.81814 102.0599 64.74094 20.58775 26.91077 18.87564 144.5287 99.4154 182.3605 73.27294 210.988 32.39081 7.011413 12.38419 10.88231 29.10665 17.87069 23.54908

P60 13.03302 10.4556 14.38211 0.729251 2.355793 0.433554 0.279997 15.05641 2.37954 4.557565 0.216411 6.332 3.211058 1.445636 1.746222 6.779031 7.014024 1.625075 5.296251 1.483792 5.215454 8.73205 10.62661 22.86664 12.90688 3.513369 0.538002 1.266776 0.74851 1.638163 0.884162 11.21035

P120 0.799618 1.584129 1.844257 0.191274 0.356542 0.063635 0.15105 2.982021 0.39273 1.109134 0.054857 1.11914 0.313049 0.282314 0.357686 1.871446 1.378947 0.667045 0.311635 0.516853 0.991146 2.08833 1.648685 1.160095 5.810562 0.6002 0.168421 0.220919 0.160919 0.243853 0.251317 0.482224

Y P180 P240 1.590897 0.78674 3.287767 0.947428 2.510149 1.156702 0.619778 0.33697 1.85544 0.215188 0.591345 0.056607 0.672018 0.127641 2.125112 1.777731 0.254617 0.186825 2.759364 1.132785 0.507005 0.055963 2.580461 0.557637 2.416768 0.237637 1.550437 0.32136 1.176331 0.257492 2.343622 2.275781 2.699051 0.866618 1.211123 0.496388 0.141988 0.148659 1.10915 0.279437 1.243368 0.752752 1.647295 1.978435 2.411724 1.440092 0.934597 0.895046 3.832087 6.546666 0.451353 0.398 0.128893 0.140015 0.116567 0.16919 0.091306 0.085282 0.14046 0.231607 1.446744 0.32983 0.717918 0.255383

P300 0.489019 0.828721 0.708921 0.102798 0.177319 0.096882 0.134062 1.541691 0.179228 0.531971 0.057709 0.326969 0.110892 0.201772 0.197382 1.361323 0.707014 0.320573 0.095363 0.203997 0.474773 0.955565 1.181513 0.655983 13.27752 0.335216 0.112188 0.057002 0.058023 0.150995 2.794379 0.292077

P360 0.247214 0.42112 0.467273 0.094555 0.091874 0.052008 0.078339 0.84471 0.132203 0.398962 0.046985 0.210025 0.097062 0.183505 0.13355 0.988302 0.377791 0.193659 0.154593 0.088192 0.400025 0.561971 4.561524 0.427867 2.720744 0.15571 0.050348 0.12016 0.032289 0.100188 0.292688 0.08798

P420 0.14543 0.291984 0.352879 0.083482 0.055746 0.048912 0.087939 0.405713 0.081587 0.395523 0.042653 0.121773 0.064786 0.103912 0.124368 0.557684 0.337941 0.109293 0.94221 0.112411 2.312365 0.707742 6.832216 0.292125 1.226398 0.218523 0.112675 0.039817 0.039962 0.105239 0.261111 0.076267

P480 0.141472 0.2364 0.229178 0.049538 0.043736 0.019229 0.033614 0.431274 0.063421 0.42095 0.02559 0.084633 0.047236 0.072537 0.075312 0.443718 0.137362 0.075677 0.108808 0.040931 28.44145 0.425957 0.484867 0.189479 1.268367 0.095768 0.034504 0.032954 0.020627 0.05777 0.075621 0.0457

Palias 0.156393 0.252044 0.251653 0.100257 0.075289 0.037278 0.06593 0.431834 0.084795 0.297139 0.039087 0.124346 0.077405 0.101846 0.099406 0.484286 0.256027 0.093694 0.335281 0.077996 11.74693 1.656191 0.523334 0.227667 1.696095 0.212089 0.105245 0.042066 0.051221 0.071367 0.16849 0.066841


fn

ID


289

ESB(Hz) 94.1473 57.02204 104.4109 111.1834 122.592 40.22477 126.3434 119.7571 29.60654 135.2358 70.85961 39.78837 101.4036 96.5311 70.8507 103.4202 107.2552 123.0635 139.958 68.3729 169.4057 161.625 166.8982 108.1661 125.5131 102.228 71.72829 59.72015 90.87758 151.5697 113.4632 127.0877

Pt 65.709 25.95147 105.9325 69.13302 18.65167 37.59793 29.48863 20.5192 17.13609 60.11243 22.47393 18.02084 18.53699 9.90285 5.201734 206.4252 22.77571 42.48457 78.17305 58.70579 36.75196 25.83086 192.6088 65.74857 68.70505 16.81966 38.82252 71.79851 76.33504 72.47033 129.4992 2.942635

P60 3.012858 7.133183 8.652943 7.918688 1.15128 16.32669 2.357443 1.346373 1.897776 4.424799 5.508804 5.128646 2.010635 1.701882 1.572332 20.58782 3.198827 2.898851 5.529087 4.29231 2.651236 1.084083 14.50511 10.56723 11.38467 2.081525 7.074018 21.62052 9.74107 2.764589 20.84073 0.349413

P120 0.724426 0.743234 1.152952 1.265731 0.236457 0.573191 0.585555 0.400348 0.164324 1.041716 0.280665 0.147703 0.244165 0.089554 0.046495 4.577964 0.436952 0.556678 1.661405 0.184242 1.196366 0.289417 5.017329 1.358474 2.048701 0.252108 0.399769 1.833432 1.221719 1.622747 2.230943 0.085756

Y P180 P240 7.502687 0.548974 0.341168 0.183175 5.895262 0.897321 5.220941 0.700832 2.421303 0.268526 1.657387 0.327981 1.403857 0.335325 1.601468 0.31845 7.29205 0.115531 0.822959 0.569554 0.370969 0.243943 0.96727 0.14461 2.07796 0.123957 0.790103 0.069824 0.499684 0.041676 2.346061 1.56651 0.437483 0.201388 1.704349 0.351086 1.836167 0.800848 1.245971 0.217466 0.850164 0.706067 0.781041 0.268114 3.992484 3.66386 1.761606 0.541744 0.860184 0.92309 1.744272 0.119302 3.019553 0.251145 1.209407 1.104713 3.071187 0.401255 1.986743 1.520693 1.300129 1.773907 0.051602 0.083519

P300 0.362125 0.226083 0.749521 0.997883 0.219385 0.347784 0.533218 0.343803 0.280464 0.711253 0.148342 0.077542 0.079246 0.273218 0.041361 0.74605 0.146552 0.313155 0.689759 0.258971 0.217172 0.198572 2.050954 0.367199 0.501728 0.272066 0.673867 0.570672 0.396231 0.702547 1.002151 0.032195

P360 0.205762 0.106606 0.348951 0.29453 0.106522 0.144318 0.119178 0.128473 0.051331 0.220462 0.113103 0.092503 0.06867 0.045112 0.032936 0.389716 0.084511 0.105332 0.292657 0.103298 0.110523 0.097828 1.076412 0.178448 0.350572 0.058996 0.092418 0.266966 0.161071 0.285536 0.513913 0.026376

P420 0.320153 0.326759 1.677324 2.031864 0.245041 0.216655 0.077431 0.161413 0.583405 0.136954 0.181673 0.08064 0.067254 0.049641 0.037158 0.292828 0.132651 0.172573 0.293524 0.149693 0.152925 0.117945 0.694125 0.209295 0.212436 0.101564 0.219986 0.281197 0.190664 0.160524 0.497293 0.044423

P480 0.101995 0.077568 0.176965 0.146116 0.063771 0.103145 0.053481 0.066197 0.022092 0.099839 0.082242 0.092454 0.038594 0.032887 0.01633 0.268771 0.043509 0.046632 0.13156 0.061813 0.059096 0.044855 0.386914 0.094402 0.119311 0.024726 0.044604 0.128189 0.075032 0.131756 0.319385 0.013473

Palias 0.128506 0.104088 0.227885 0.264508 0.105409 0.174904 0.093271 0.159739 0.037792 0.148631 0.112922 0.160078 0.086935 0.047089 0.032356 0.230912 0.049107 0.053727 0.126383 0.072068 0.063981 0.05442 0.412248 0.111094 0.121564 0.036476 0.071707 0.15708 0.105912 0.137998 0.352062 0.024589


290

fn

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128


WC(dB) -4.65691 -4.17394 -4.15533 -5.20734 -4.74034 -6.5643 -3.84903 -7.73044 -4.26609 -8.16872 -5.41982 -4.08174 -5.97236 -5.1111 -6.71483 -5.76791 -5.28732 -5.54817 -5.20991 -4.88622 -5.94707 -4.91035 -5.38676 -4.71098 -3.08016 -4.2546 -4.50976 -4.75145 -7.63984 -4.81061 -4.39378 -5.31346

ESB(Hz) 122.7698 154.3244 102.2352 119.6958 111.904 93.65244 119.9964 62.10713 150.87 68.93427 111.4164 103.1877 114.711 83.09535 93.455 110.1549 140.4806 130.3481 60.37773 122.6534 126.1535 121.9633 129.8404 140.9418 173.6933 125.7365 150.8286 122.753 73.25458 155.9147 169.4584 87.68865

Pt 20.87441 14.5442 21.03319 43.15337 91.16406 38.12228 4.202458 30.50338 64.56394 61.11815 40.65811 12.11353 32.89192 44.49317 35.49228 52.59954 33.19346 43.09526 118.0011 31.02374 102.7383 35.41971 177.3289 66.76293 113.8636 81.65952 79.05914 40.20082 102.8076 26.55381 81.64074 39.57901

P60 2.691651 1.3283 0.968934 2.57976 4.195484 1.641127 0.196712 2.749999 5.154559 3.492151 3.025449 0.453038 3.520052 6.757341 7.275587 3.15007 2.277476 4.638854 17.29614 2.436573 11.70647 1.42048 5.99523 4.380618 18.9832 3.812259 3.172739 2.513672 4.174758 3.717525 3.65815 2.987251

P120 0.482663 0.420592 0.535042 0.827415 1.226771 0.243261 0.085002 0.594569 1.9387 0.651595 0.476445 0.131797 0.619952 0.815244 0.568226 0.743346 0.636594 0.997462 0.456021 0.78113 2.494144 0.521622 1.381974 1.464491 2.115987 2.535672 0.93561 0.726541 0.664986 1.316451 2.417936 0.393558

Y P180 P240 0.548591 0.269266 0.694692 0.170622 2.422897 0.32789 1.398983 0.416978 1.633853 0.928911 0.426848 0.124415 0.201426 0.046139 0.812783 0.326217 1.098247 1.13343 0.744176 0.287313 0.573763 0.302525 1.265521 0.124196 1.019302 0.248608 1.049439 0.408972 0.814159 0.264142 1.916828 0.49241 1.593454 0.262149 1.737052 0.453538 4.681244 1.517948 1.562558 0.72537 1.346774 0.883013 1.137857 0.331565 0.575788 0.625267 0.829563 0.781609 6.54598 9.388741 2.101159 1.919117 0.679813 0.633298 0.449931 0.413609 1.645824 0.33313 0.436028 0.47644 1.115543 0.962562 1.09502 0.627062

P300 0.146188 0.14007 0.332568 0.343511 0.646275 0.073667 0.041053 0.237333 0.648371 0.154099 0.129539 0.093941 0.154225 0.216609 0.164906 0.39523 0.184574 0.276682 0.741503 0.435387 0.490053 0.231236 0.307065 0.441691 2.050648 0.81672 0.310008 0.230123 0.231829 0.298677 0.544038 0.229537

P360 0.082942 0.076466 0.099029 0.130063 0.311832 0.051755 0.022426 0.149652 0.37974 0.097307 0.064537 0.062261 0.086713 0.132208 0.079428 0.133919 0.076855 0.129111 0.181213 0.205138 0.220271 0.107679 0.189187 0.210774 0.716551 0.381939 0.156286 0.14736 0.128672 0.148961 0.282272 0.169375

P420 0.104585 0.08702 0.105217 0.11014 0.26024 0.06922 0.043379 0.089776 0.223014 0.184971 0.07539 0.067356 0.057228 0.085282 0.049539 0.069794 0.035483 0.091049 0.970791 0.131168 0.174686 0.07233 0.158982 0.195835 18.19075 0.219534 0.082211 0.079745 0.083996 0.084572 0.162894 0.137946

P480 0.036325 0.031779 0.058943 0.06266 0.175471 0.025277 0.014065 0.050333 0.11814 0.043034 0.031464 0.036733 0.045188 0.062954 0.038492 0.056661 0.036815 0.059733 0.186938 0.094572 0.128043 0.059999 0.096262 0.102892 1.310699 0.1653 0.067729 0.065412 0.065447 0.062277 0.134892 0.113502

Palias 0.043057 0.038216 0.113619 0.099394 0.23142 0.037341 0.025804 0.077263 0.149375 0.055615 0.070723 0.05946 0.061501 0.087398 0.067119 0.078941 0.061736 0.091427 0.443235 0.110475 0.156244 0.073121 0.090624 0.116418 3.858349 0.19909 0.073985 0.071428 0.110073 0.071282 0.178796 0.120034


fn 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

291

ID


ESB(Hz) 146.8604 119.9572 119.0909 108.9027 97.49026 170.7088 129.8548 156.8595 93.92482 129.632 97.34124 116.1626 133.6458 178.1788 78.36756 67.48998 31.98192 80.35237 26.21547 89.47535 107.662

Pt 25.16081 28.71128 153.5331 54.90108 28.07605 17.86135 25.51467 17.34918 18.77649 21.0099 100.3651 29.51802 14.71078 34.27096 32.47581 12.94981 11.02885 20.50079 10.91902 18.68898 56.24707

P60 1.66251 1.423197 16.15819 5.759536 3.338391 1.518241 0.778732 1.055254 0.974412 0.792173 5.084716 1.149811 2.111301 1.847504 1.115639 1.597979 0.833162 3.360128 0.841272 0.96155 6.607488 11.74726

P120 0.624252 0.558481 3.357907 0.740573 0.338896 0.445484 0.334228 0.558471 0.212818 0.240173 1.436544 0.519883 0.243503 0.488766 0.191511 0.154619 0.097771 0.208297 0.074689 0.307899 1.156848 2.056725

Y P180 P240 0.367922 0.395071 0.335775 0.358668 2.674586 0.80151 4.630783 0.630045 4.30174 0.239691 1.937608 0.325359 2.143631 0.21795 1.223145 0.270436 2.436689 0.169849 2.048091 0.200604 3.023954 1.376901 1.738469 0.651147 1.812973 0.169842 3.590599 0.595685 2.876244 0.115995 2.933328 0.160966 3.316765 0.081346 2.947711 0.148716 3.414662 0.059888 3.125203 0.190963 1.536428 0.69608 2.73157 1.23754

P300 0.217115 0.201674 0.426534 0.399711 0.193403 0.267169 0.18799 0.12024 0.107127 0.128233 0.760528 0.524251 0.129525 0.444051 0.058154 0.076322 0.050723 0.117477 0.060816 0.159459 0.526927 0.936807

P360 0.118797 0.119724 0.286233 0.233492 0.088728 0.139605 0.08724 0.084326 0.077835 0.086351 0.428052 0.367881 0.074083 0.267179 0.04388 0.045027 0.033957 0.043364 0.024164 0.0787 0.26638 0.473589

P420 0.106334 0.096373 0.186682 0.254678 0.145617 0.116696 0.054953 0.071519 0.068934 0.060416 0.250767 0.232686 0.057707 0.181975 0.054517 0.057395 0.021551 0.087474 0.066202 0.167059 0.425451 0.756397

P480 0.052127 0.060627 0.129002 0.148103 0.042655 0.075289 0.038955 0.044142 0.033461 0.038145 0.209303 0.186537 0.034696 0.117381 0.022286 0.025311 0.014633 0.025371 0.011935 0.035088 0.346914 0.616768

Palias 0.063369 0.073193 0.142516 0.163416 0.067526 0.07862 0.069176 0.049874 0.053286 0.068616 0.208779 0.199529 0.062815 0.148117 0.068551 0.07719 0.053088 0.061227 0.036365 0.04863 0.27677 0.492061


292

fn

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


Z WC(dB) -9.57214 -8.65062 -7.32982 -9.06 -6.19824 -7.42745 -3.75161 -5.7494 -6.81764 -9.23954 -5.27794 -3.84446 -5.49093 -2.15968 -7.59391 -5.13243 -6.67613 -4.93003 -4.99874 -4.91985 -3.57203 -4.18853 -4.96127 -5.11798 -8.00578 -6.07474 -5.49345 -5.78558 -4.31731 -4.88666 -2.70143 -5.71706

ESB(Hz) 21.9091 52.62954 106.6772 79.21945 101.1585 56.26429 125.7838 17.83516 51.01423 20.88235 82.93279 97.99382 50.90076 192.6685 79.88808 76.60999 31.39091 94.07037 98.62032 104.6477 132.5946 139.541 29.63376 80.34815 13.39707 48.82623 112.1704 94.78834 123.7053 92.69411 128.4831 109.9098

Pt 4.634101 118.8478 54.64728 121.6994 116.1752 74.40878 10.93737 28.04109 32.61639 65.44856 21.27028 15.11761 4.912969 10.44741 220.1141 184.0391 16.48165 11.90641 111.4487 83.34343 27.9543 24.7541 18.23529 5.94681 18.7785 35.23481 89.9606 4.835604 18.89381 13.35078 20.75616 31.21495

P60 4.211798 5.260862 6.247842 7.365539 7.316985 14.62401 0.955118 0.629093 2.151156 27.90442 1.247213 0.955379 0.079598 0.359188 14.41327 10.20282 0.689155 2.213518 14.31767 8.832618 2.423342 0.817643 1.229527 0.639286 11.08532 14.57313 9.539288 1.365969 0.618941 2.66997 0.662086 2.623226

P120 0.169751 0.88136 1.15719 1.384511 1.211984 19.125 0.209952 0.21543 0.184071 0.238428 0.778811 0.222923 0.035915 0.17227 1.614573 1.784326 0.283801 0.238154 1.348868 1.423949 0.483497 0.279477 0.22623 0.082926 0.108202 5.363412 1.793773 0.277955 0.130189 0.143773 0.28933 0.445492

P180 0.087627 0.42788 1.554067 1.641174 0.975177 5.881856 0.440645 0.388931 0.482438 1.015815 0.369591 0.682691 0.845222 0.801132 2.029339 2.784891 0.170316 0.2374 1.182223 1.243528 1.444029 2.696624 0.419522 0.164167 0.369757 0.36842 2.52813 0.20002 0.110904 0.403899 1.075181 2.259484

P240 0.043654 0.333582 0.874934 0.574137 0.684148 0.5542 0.603734 0.211907 0.210193 0.204612 1.493277 0.718037 0.040345 0.243263 0.901361 1.632841 0.119667 0.171106 0.891683 0.666965 0.54808 0.167569 0.169099 0.056439 0.084646 0.319645 0.752403 0.139725 0.089258 0.148419 0.380619 0.319096

P300 0.029297 0.22672 0.269916 0.239623 0.361819 0.287247 0.095671 0.16213 0.168119 0.111766 1.012636 0.469658 0.041418 0.41013 0.554134 1.208636 0.122616 0.094428 0.574998 0.513242 0.375511 0.272744 0.200996 0.090252 0.087617 0.191328 0.520134 0.09857 0.068504 0.108005 0.277408 0.148083

P360 0.010252 0.160865 0.122187 0.18462 0.249514 0.179236 0.080937 0.142024 0.142604 0.080368 0.652182 0.373814 0.037062 0.299664 0.454756 0.846862 0.08942 0.06257 0.410809 0.353179 0.274012 0.113291 0.143109 0.037683 0.048808 0.145084 0.353935 0.076326 0.052357 0.071082 0.224454 0.074978

P420 0.013964 3.23E-07 0.048741 0.087592 0.017413 0.029284 0.149295 0.059291 0.093757 0.19832 1.311995 0.366293 0.125171 0.198581 0.401803 0.545547 0.097096 0.200809 0.726904 2.544955 0.200776 0.010075 0.187413 0.062881 0.058803 11.59501 0.544279 0.063665 0.074447 0.076333 0.090674 0.086733

P480 0.002985 0.106689 0.025494 0.042111 0.171052 0.16071 0.041104 0.067174 0.092719 0.073713 0.542905 0.283695 0.049196 0.090089 0.220166 0.397503 0.08022 0.038153 0.232172 0.215221 0.159057 0.047365 0.085834 0.015057 0.027366 0.073431 0.218048 0.034478 0.024018 0.049472 0.140738 0.060363

Palias 0.003125 0.112717 0.033902 0.046691 0.154838 0.193658 0.136044 0.086875 0.104536 0.088366 0.356011 0.315643 0.070715 0.11263 0.244775 0.460145 0.056777 0.058451 0.275516 0.23519 0.163724 0.077917 0.150097 0.025901 0.040361 0.130715 0.219661 0.051044 0.042248 0.044645 0.170645 0.065834


293

fn

ID

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64


Z WC(dB) -3.76556 -5.5787 -3.11587 -4.92659 -4.02609 -3.67734 -3.51427 -4.17224 -2.99952 -4.07422 -3.06065 -5.3018 -4.70516 -4.80745 -7.81746 -3.315 -3.96995 -4.29513 -6.46269 -3.07215 -5.81837 -3.31522 -3.50381 -3.66009 -6.07119 -4.15755 -3.64443 -7.42901 -7.26726 -1.62152 -5.90534 -6.60625

ESB(Hz) 128.1565 82.26372 136.2356 61.73728 135.7276 107.0504 117.8542 111.6818 157.693 113.2826 164.6278 110.6721 90.24773 80.14558 66.37934 138.8891 137.3978 92.73569 112.332 155.9565 81.23444 151.3025 128.2303 109.0984 73.07954 115.1234 132.5413 24.11193 75.93888 243.2232 79.17032 75.89981

Pt 18.72838 78.29424 31.73282 20.95557 8.246186 5.330315 10.83344 113.2871 10.67467 37.18887 3.205814 42.05444 28.20329 34.5957 71.0481 55.9497 28.18428 27.39942 110.4081 7.793648 149.7114 73.72956 96.56315 73.79814 710.0792 2.545446 2.647098 22.12377 59.75243 6.349132 42.37134 96.60011

P60 1.321935 3.264735 1.470736 6.542106 0.699421 0.270565 0.41662 7.138408 0.694018 1.649573 0.223292 3.990559 3.176261 6.230943 3.61232 3.246537 5.496626 2.363335 10.75671 0.593871 6.720521 4.128591 4.413104 17.00755 151.778 0.14397 0.194082 0.636219 3.216445 0.312383 9.120916 10.32458

P120 0.30596 0.827937 0.663203 0.457028 0.138705 0.057824 0.148852 2.609077 0.361788 0.658663 0.039068 1.067579 0.254301 0.241327 0.304871 1.595022 1.02774 0.316142 2.105447 0.124764 0.461579 1.381235 1.300699 2.160752 20.17637 0.048662 0.039834 0.271592 1.121893 0.156478 0.962198 0.928797

P180 1.821142 1.391414 1.043814 0.724746 0.632393 0.317603 0.458713 1.447136 0.232052 0.624004 0.308346 0.78861 3.661047 3.107479 1.164897 1.137024 1.793108 1.073969 0.469188 0.622647 0.906168 0.918958 1.206924 1.405892 4.112728 0.031304 0.032718 0.108242 0.232056 0.136652 5.205165 0.881677

P240 0.239784 0.717767 0.63801 0.819509 0.117617 0.128073 0.177761 2.203851 0.286595 0.723204 0.065382 0.534915 0.446699 0.476601 0.306861 1.250868 1.074115 0.325079 0.42049 0.119686 0.489113 2.402588 1.160923 1.440049 8.011844 0.041896 0.036907 0.133228 0.319577 0.163395 0.259379 0.232752

P300 0.217114 0.466068 0.461333 0.187678 0.074044 0.06052 0.143016 1.377517 0.207924 0.292335 0.060841 0.268266 0.257678 0.309989 0.166764 0.898233 0.721012 0.311082 0.256854 0.146902 0.461146 1.010721 0.767002 1.000351 16.35247 0.022504 0.024959 0.093602 0.17754 0.133149 1.555146 0.144444

P360 0.139679 0.311454 0.311226 0.120068 0.063399 0.066448 0.094547 1.08739 0.130301 0.311568 0.05608 0.227805 0.10399 0.163301 0.137707 0.651913 0.382005 0.256904 0.154267 0.062347 0.327553 0.453907 4.382973 0.697844 3.994628 0.016593 0.018205 0.065094 0.139775 0.084293 0.131086 0.091566

P420 0.166111 0.286561 0.328814 0.142492 0.074504 0.075272 0.065009 0.515718 0.093941 0.177939 0.038358 0.507815 0.252644 0.289321 29.62208 0.364985 0.482102 0.130054 0.267107 0.085281 9.051268 0.608586 11.38451 0.464521 2.883638 0.190847 0.175024 0.134063 0.128911 0.078465 0.297593 0.402696

P480 0.067372 0.177214 0.148423 0.071925 0.026019 0.031143 0.042393 0.389927 0.069859 0.141971 0.019156 0.09407 0.05156 0.091748 0.081893 0.2152 0.1658 0.095766 0.094198 0.028834 22.28571 0.445813 0.496059 0.450188 1.131867 0.009757 0.010247 0.036363 0.075102 0.052024 0.092797 0.048403

Palias 0.097724 0.163949 0.209114 0.093802 0.048018 0.044677 0.054142 0.425681 0.085569 0.149395 0.027618 0.111917 0.097908 0.139489 0.10555 0.22867 0.215811 0.120166 0.218052 0.05097 8.581949 2.172185 0.47667 0.436627 1.616702 0.01426 0.015729 0.03852 0.083431 0.054253 0.109773 0.056796


fn

ID


294

Z ESB(Hz) 160.4946 184.9285 113.6536 106.7954 98.95982 170.3096 118.4383 117.7833 38.98434 137.2577 139.7858 78.76705 69.7387 98.3421 63.68849 93.47862 70.05877 109.785 181.5908 91.57731 154.7025 108.4076 143.2405 127.7886 137.4785 102.1476 71.54495 125.3844 125.1205 180.6273 76.36257 90.15362

Pt 14.87432 16.12722 28.81591 14.69914 9.936272 26.7604 13.53576 21.45559 11.51536 283.3842 6.650851 10.03382 14.73019 6.134871 19.3371 11.6752 10.73447 24.61704 17.98534 12.44699 8.33452 166.2162 32.90282 110.6217 192.0901 16.90989 42.31035 59.74799 68.93473 24.24742 144.3106 2.534557

P60 1.03713 1.108922 2.541779 0.680294 0.245831 3.61062 0.989204 1.481937 0.706214 20.04341 1.331785 0.987972 2.374408 0.885893 3.791249 2.691911 3.378368 1.184771 0.930376 1.9462 1.035209 3.326377 2.962473 5.465143 16.00662 0.763782 1.322793 5.976599 7.79091 1.177301 32.06177 0.592382

P120 0.322913 0.31554 0.360311 0.196441 0.062896 0.470121 0.180241 0.35053 0.038605 6.926169 0.117464 0.081286 0.098527 0.05057 0.105286 0.155557 0.158522 0.161306 0.26054 0.107725 0.171433 1.023778 0.493005 1.59288 4.517136 0.173057 0.270801 1.080222 1.550913 0.390662 1.792966 0.05159

P180 2.917461 0.334155 0.76768 0.582717 0.522296 0.749253 0.357648 0.833943 0.109711 5.385745 0.411045 1.244175 1.445758 0.591707 0.796303 0.858205 0.199975 0.936437 0.69099 0.753021 0.221889 0.923838 0.958522 1.505472 1.262334 0.781216 0.95052 0.856243 1.338996 0.998622 2.545249 0.073661

P240 0.321347 0.422483 0.454607 0.299295 0.126993 0.760362 0.182823 0.259965 0.039047 2.220843 0.121172 0.103798 0.068578 0.043529 0.079099 0.150859 0.151668 0.161439 0.388211 0.123842 0.166099 0.859151 0.724991 0.714978 1.066309 0.143964 0.156538 0.688539 0.464201 0.530952 2.754233 0.034236

P300 0.258174 0.362406 0.543926 0.197102 0.101296 0.784805 0.687229 0.900732 0.006205 1.308459 0.081193 0.072267 0.059555 0.032329 0.072562 0.082146 0.10636 0.113341 0.263808 0.117639 0.10976 0.515563 0.51534 0.384365 0.67568 0.087315 0.098397 0.391626 0.255331 0.43528 1.841688 0.046645

P360 0.195263 0.26407 0.378134 0.149261 0.070132 0.499493 0.093498 0.149301 0.005933 0.659654 0.08436 0.08726 0.048539 0.027661 0.064418 0.058575 0.083652 0.066167 0.163018 0.073351 0.061153 0.347294 0.389023 0.226335 0.424167 0.060664 0.071062 0.33416 0.168194 0.34899 1.285731 0.021288

P420 0.223134 0.13867 0.815222 0.49214 0.283398 0.208298 0.132442 0.172955 1.415007 0.306418 0.308731 0.237979 0.094669 0.044824 0.04779 0.067375 0.068344 0.10009 0.359864 0.046721 0.060859 0.071939 0.286072 0.097275 0.295302 0.057735 0.090619 0.189864 0.062924 0.145953 0.175891 0.03939

P480 0.108183 0.161721 0.249715 0.080363 0.048159 0.274151 0.051542 0.080218 0.003194 0.389389 0.055617 0.082385 0.029651 0.01899 0.037119 0.029354 0.043547 0.02665 0.070379 0.043995 0.038966 0.143887 0.188266 0.106408 0.168389 0.035368 0.039342 0.164455 0.079069 0.175601 0.885261 0.0146

Palias 0.145035 0.155986 0.223214 0.092303 0.101572 0.229275 0.100253 0.2265 0.006508 0.32038 0.080066 0.159769 0.041305 0.027158 0.064776 0.041839 0.070537 0.049729 0.097317 0.064319 0.071099 0.180883 0.198104 0.115586 0.205299 0.048766 0.04587 0.179286 0.101619 0.161503 0.893647 0.018386


295

fn

ID

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128


Z WC(dB) -4.74472 -5.2741 -7.14064 -3.57585 -2.05407 -2.13934 -3.42751 -2.6253 -4.52432 -7.7721 -6.87208 -4.08948 -7.85931 -8.46695 -7.49694 -7.17021 -6.12546 -6.23509 -3.6706 -4.65747 -5.56581 -8.56067 -6.34956 -3.74146 -3.83885 -4.39977 -4.37664 -3.32401 -4.90446 -5.39546 -4.32893 -2.23758

ESB(Hz) 111.4065 102.1693 73.68592 134.8875 196.6838 168.882 116.7738 146.0687 128.7518 98.66612 69.98797 82.20793 20.72791 12.91592 57.70205 44.0465 112.3444 60.84457 45.81732 87.93838 61.56187 75.9569 92.99674 120.7428 172.3685 124.3035 101.5237 151.9309 109.5121 116.6412 147.9491 185.4113

Pt 9.891321 32.3661 59.30293 9.891148 39.36149 7.44547 4.124017 13.23262 66.08708 63.14329 136.6776 18.5808 39.54006 51.09103 37.94849 54.70153 36.63363 70.72383 19.24203 55.0153 144.4617 155.7668 170.5789 20.06268 97.91964 103.8567 48.92206 15.14373 36.72552 41.43693 77.38338 17.71791

P60 0.906136 2.16034 2.844567 0.524754 1.639502 0.200528 0.246339 0.779656 7.606721 7.38063 1.533919 0.768483 18.93219 33.49809 9.706866 13.45609 6.080297 11.35411 4.424073 9.553236 23.00939 6.300929 6.917779 1.685789 13.31051 7.757018 2.572836 1.997408 1.383879 4.977693 7.536088 1.196142

P120 0.165356 0.441678 0.679145 0.168062 0.513953 0.067404 0.063499 0.189222 0.978578 0.638196 0.348711 0.153192 0.200191 0.270634 0.418208 0.54369 0.599604 0.526228 0.149876 0.67875 1.385379 0.642004 1.12094 0.299164 4.380922 1.682967 0.361765 0.303508 0.231983 0.784631 1.629218 0.233679

P180 0.358257 0.620767 1.156152 0.998027 0.944381 0.227057 0.211151 0.380392 0.776898 0.6012 0.386596 1.116221 0.774275 0.640001 1.810478 2.7911 1.34971 3.851792 0.539153 2.86385 2.888547 1.836827 0.707631 0.30504 3.216968 1.271717 0.381885 0.368509 1.298543 0.578277 0.907656 1.217785

P240 0.117445 0.279566 0.320281 0.185319 0.631987 0.091254 0.065973 0.434422 1.192823 0.2901 0.172657 0.247207 0.24617 0.306886 0.221199 0.217188 0.262721 0.675127 0.206282 0.584113 0.884339 0.352794 0.50651 0.227094 1.924716 1.088294 0.233312 0.245068 0.192715 0.48313 0.941919 0.389791

P300 0.069755 0.167542 0.218932 0.31965 0.525751 0.07822 0.048208 0.177696 0.403151 0.167107 0.117058 0.222194 0.268663 0.23622 0.142208 0.189604 0.192729 0.252492 0.167081 0.446235 0.662008 0.197833 0.295073 0.179197 0.948434 0.762386 0.171174 0.197987 0.138741 0.316883 0.579107 0.319721

P360 0.047257 0.12304 0.138806 0.066571 0.324286 0.060137 0.037842 0.174031 0.315004 0.092784 0.077296 0.133345 0.081564 0.11111 0.072351 0.104919 0.09279 0.125819 0.115225 0.273899 0.356091 0.130377 0.204637 0.147302 0.556131 0.443348 0.101006 0.118549 0.088517 0.196732 0.436457 0.202379

P420 0.095526 0.053258 0.12855 0.076712 0.314978 0.081608 0.061411 0.22553 0.104655 0.065328 0.07904 0.123368 0.13167 0.163252 0.147971 0.10456 0.204352 0.340339 0.26508 0.175903 1.451577 0.144286 0.167146 0.57945 0.414105 0.181664 0.14915 0.172338 0.138982 0.084471 0.273574 0.184311

P480 0.023338 0.073555 0.094047 0.027686 0.181319 0.033622 0.030213 0.071637 0.188563 0.049994 0.038358 0.058137 0.048926 0.069701 0.034969 0.054346 0.041318 0.093899 0.09596 0.1188 0.192252 0.081921 0.089003 0.08472 0.267487 0.215386 0.04322 0.049564 0.041151 0.085687 0.183898 0.120809

Palias 0.028465 0.079411 0.081622 0.044728 0.199367 0.034647 0.029721 0.093077 0.184201 0.064944 0.048735 0.067067 0.053698 0.071527 0.057321 0.072 0.055192 0.110495 0.076786 0.149443 0.185066 0.092524 0.107879 0.093693 0.427105 0.233576 0.060496 0.075097 0.060222 0.092783 0.2329 0.137862


fn 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

296

ID


Z ESB(Hz) 144.3381 164.4143 97.84376 90.66195 87.68194 84.24351 50.71126 77.83918 132.2208 96.3542 127.5408 111.3294 81.6648 91.68456 73.37234 40.68977 50.59283 64.37234 51.46294 58.24826 103.9095

Pt 46.95782 176.3141 30.49993 73.97808 23.73967 68.97205 34.32557 13.86773 28.12145 9.112447 35.61912 26.80969 23.313 28.4137 9.921843 17.52136 10.18395 14.89254 13.36626 21.75835 53.82467

P60 4.21409 10.45945 1.36479 3.798407 2.301573 8.239817 8.200281 2.911169 2.710786 1.429678 2.060083 1.207465 3.017014 4.423236 2.960704 5.694484 1.834851 2.517592 4.470051 7.644719 6.172602 11.46798

P120 1.610656 3.839518 0.241484 0.845322 0.171792 0.415094 0.287049 0.132573 0.389401 0.077664 0.346427 0.425043 0.200409 0.35475 0.08425 0.11562 0.08418 0.133163 0.068486 0.126799 1.013263 1.882525

P180 0.856547 1.962117 0.936387 2.474821 1.628945 1.669807 0.989429 0.581545 1.228466 0.903361 1.54511 1.18594 1.521273 1.752851 1.139769 1.754432 1.429456 1.608368 1.551677 1.418234 1.11952 2.079938

P240 1.01876 1.657275 0.187034 0.812971 0.19192 0.409988 0.195283 0.172482 0.362139 0.094164 0.52929 0.477798 0.305747 0.418288 0.077788 0.126533 0.069894 0.091472 0.048984 0.161639 0.543678 1.010091

P300 0.533475 0.943966 0.17525 0.70299 0.236473 0.409808 0.268765 0.161699 0.282075 0.099986 0.399439 0.392615 0.319243 0.56668 0.183467 0.286197 0.162188 0.273611 0.211879 0.304026 0.459245 0.853224

P360 0.349218 0.530401 0.115361 0.533295 0.099718 0.212738 0.093736 0.062718 0.133064 0.04799 0.316852 0.247814 0.135854 0.230676 0.031212 0.048714 0.028859 0.039179 0.027778 0.078598 0.268547 0.498929

P420 0.094672 0.083976 0.088769 0.177458 0.109072 0.136855 0.158378 0.069281 0.074273 0.074747 0.26443 0.166466 0.053167 0.189582 0.057499 0.073596 0.091457 0.199766 0.080553 0.181967 0.729852 1.355979

P480 0.182633 0.244537 0.054398 0.328474 0.047292 0.110243 0.052531 0.037837 0.066244 0.027099 0.166249 0.145809 0.051153 0.104644 0.016192 0.02656 0.011954 0.018313 0.015166 0.044213 0.295327 0.548683

Palias 0.185395 0.287913 0.060796 0.351386 0.049339 0.111774 0.072153 0.046384 0.071097 0.033827 0.190483 0.179216 0.069461 0.135626 0.029888 0.037222 0.025297 0.033018 0.026111 0.050163 0.223096 0.414487


Appendix F. Interference cancellation evaluation

signal noise trial var 0 s 0 sn 201.539 se1 69.0447 n1 se2 571.208 se3 161.82 se4 24.3363 sn 201.554 se1 69.5669 n2 se2 571.397 se3 162.021 fp11x se4 23.3879 sn 32.2463 se1 47.5381 n3 se2 570.943 se3 161.543 se4 8.70935 sn 32.2487 se1 47.7478 n4 se2 570.966 se3 161.573 se4 8.17108 0 s 0 sn 201.544 se1 83.9514 n1 se2 303.787 se3 106.211 se4 33.3952 sn 201.588 se1 84.4885 n2 se2 303.974 se3 106.414 fp15y se4 31.4033 sn 32.2471 se1 61.7458 n3 se2 303.639 se3 105.955 se4 9.09549 sn 32.2541 se1 61.962 n4 se2 303.66 se3 105.986 se4 9.7913 0 s 0 sn 201.555 se1 42.0396 n1 se2 112.805 se3 31.4224 se4 26.02 sn 201.561 se1 41.7059 n2 se2 113.005

bias 0 13.171 6.153359 13.5681 7.957436 3.811141 13.13575 6.172051 13.57453 7.970223 3.752063 5.268401 4.594236 13.55908 7.940032 2.317234 5.254302 4.608368 13.55965 7.942002 2.237953 0 13.17133 6.220294 9.989581 6.159509 4.305631 13.13632 6.236819 9.998557 6.176266 4.123155 5.268534 4.47893 9.980045 6.137347 2.331207 5.254528 4.490709 9.981062 6.140011 2.391919 0 13.17244 5.255025 6.872343 4.060555 3.983222 13.13547 5.226152 6.885501

niso QRSd LASd RMS40 Comments 1.113 108 44 3.5027 1.449 108 46 3.4071 1.483 106 43 2.4766 2.542 93 44 2.4042 1.754 104 42 3.0668 1.146 109 45 3.4043 1.449 107 45 3.3594 1.484 106 43 2.4647 2.541 93 44 2.4038 1.754 104 42 3.0661 1.145 109 45 3.3661 1.152 110 46 3.4121 1.593 105 42 2.8468 2.539 93 44 2.4037 1.752 104 42 3.0651 1.136 109 45 3.4112 1.15 110 46 3.3903 1.596 105 42 2.8396 2.539 93 44 2.4035 1.752 104 42 3.0649 1.131 109 45 3.41 1.629 118 63 1.6302 1.783 119 64 1.5615 1.968 118 63 1.6864 3.24 106 63 1.6304 2.002 119 64 1.7889 1.614 118 63 1.5777 1.801 119 64 1.5348 1.979 118 63 1.7008 3.242 106 63 1.6313 2.003 119 64 1.7939 1.609 118 63 1.6065 1.708 120 65 1.4809 1.955 118 63 1.6359 3.237 106 63 1.63 2.003 119 64 1.7861 1.646 120 65 1.4988 1.716 120 65 1.4662 1.958 118 63 1.6433 3.237 106 63 1.6303 2.003 119 64 1.7881 1.653 120 65 1.4834 0.467 96 31 23.229 0.775 94 30 22.979 0.927 90 28 23.543 0.669 93 29 23.996 0.728 156 93 0.6594 0.544 94 30 23.386 0.75 94 30 22.958 0.914 91 29 23.755 0.671 93 29 23.996

297


signal noise trial var se3 31.6347 fp33x se4 25.0466 sn 32.2488 se1 19.8954 n3 se2 112.627 se3 31.1666 se4 11.0424 sn 32.2497 se1 19.7622 n4 se2 112.654 se3 31.2014 se4 11.1419 0 s 0 sn 201.678 se1 60.1706 n1 se2 171.819 se3 54.1629 se4 33.0086 sn 201.718 se1 59.8698 n2 se2 172.001 se3 54.3635 fp40z se4 32.0216 sn 32.2684 se1 37.9285 n3 se2 171.616 se3 53.8885 se4 15.3516 sn 32.2749 se1 37.8082 n4 se2 171.636 se3 53.9191 se4 16.0885 0 s 0 sn 201.682 se1 155.48 n1 se2 1183.73 se3 331.34 se4 25.4679 sn 201.616 se1 154.171 n2 se2 1183.93 se3 331.566 fp62z se4 23.267 sn 32.269 se1 131.616 n3 se2 1183.47 se3 331.048 se4 7.18891 sn 32.2586 se1 131.091

bias 4.082114 3.89587 5.268977 3.460161 6.855654 4.033593 2.578088 5.254189 3.449222 6.85753 4.037178 2.586279 0 13.17705 6.200795 8.753989 5.415281 4.534423 13.1419 6.176356 8.762565 5.428823 4.453013 5.270821 4.825046 8.74457 5.397313 3.102095 5.256759 4.81472 8.745611 5.399365 3.141172 0 13.17675 9.480755 19.09641 11.49047 3.92443 13.13775 9.444732 19.1038 11.50221 3.754672 5.2707 8.387995 19.08706 11.47573 2.105595 5.255101 8.374843

niso QRSd LASd RMS40 Comments 0.729 156 93 0.6573 0.543 94 30 23.309 0.64 94 30 23.159 0.771 91 28 23.535 0.666 93 29 24 0.725 156 93 0.6591 0.525 95 30 23.273 0.634 94 30 23.151 0.768 91 28 23.526 0.667 93 29 24 0.726 156 93 0.6581 0.47 96 31 23.228 0.384 74 22 21.421 0.474 66 22 21.257 0.69 68 16 20.492 0.478 118 73 1.3467 0.776 68 16 20.739 0.376 66 21 21.37 0.474 66 22 21.245 0.689 68 16 20.48 0.478 118 73 1.3476 0.778 68 16 20.739 0.366 74 22 21.435 0.4 67 22 21.37 0.718 68 16 20.484 0.478 118 73 1.3492 0.775 68 16 20.734 0.385 74 23 21.389 0.394 67 22 21.365 0.718 68 16 20.48 0.478 118 73 1.3495 0.776 68 16 20.734 0.38 74 23 21.393 0.521 100 39 21.674 0.853 83 22 93.273 6.229 64 1 77.118 10.28 65 0 79.409 6.327 64 1 78.164 0.548 98 37 54.33 0.896 109 22 93.325 6.204 64 1 77.131 10.29 65 0 79.414 6.33 64 1 78.168 0.545 98 37 54.355 0.661 83 22 93.253 6.208 64 1 77.172 10.28 65 0 79.407 6.326 64 1 78.162 0.502 99 38 39.624 0.651 83 22 93.274 6.198 64 1 77.177

298


signal noise trial var n4 se2 1183.49 se3 331.089 se4 7.38842 0 s 0 sn 201.668 se1 162.218 n1 se2 1519.78 se3 387.606 se4 26.4615 sn 201.624 se1 161.695 n2 se2 1519.98 se3 387.842 fv11x se4 24.5291 sn 32.2669 se1 139.135 n3 se2 1519.51 se3 387.302 se4 9.61783 sn 32.2598 se1 138.925 n4 se2 1519.54 se3 387.347 se4 9.58887 0 s 0 sn 201.668 se1 162.218 n1 se2 1508.99 se3 381.316 se4 26.8381 sn 201.624 se1 161.695 n2 se2 1509.21 se3 381.525 fv11z se4 25.8541 sn 32.2669 se1 139.135 n3 se2 1508.72 se3 381.019 se4 9.59891 sn 32.2598 se1 138.925 n4 se2 1508.76 se3 381.053 se4 9.6035 0 s 0 sn 201.594 se1 178.785 n1 se2 1289.68 se3 341.856 se4 19.3032

bias 19.08803 11.47783 2.139741 0 13.17647 9.352814 21.49562 12.0017 4.013943 13.13826 9.325265 21.50196 12.01213 3.885741 5.270588 8.297392 21.48657 11.98706 2.456937 5.255304 8.285292 21.48738 11.98877 2.437455 0 13.17647 9.352814 21.40404 11.91127 4.081748 13.13826 9.325265 21.40986 11.9217 3.990987 5.270588 8.297392 21.3973 11.89684 2.452547 5.255304 8.285292 21.39789 11.89845 2.436439 0 13.17392 9.81852 18.13491 11.23072 3.398938


299


signal noise trial var sn 201.557 se1 178.225 n2 se2 1289.81 se3 342.013 fv25y se4 18.0485 sn 32.2551 se1 152.886 n3 se2 1289.22 se3 341.445 se4 4.29466 sn 32.2492 se1 152.661 n4 se2 1289.22 se3 341.458 se4 3.96097 0 s 0 sn 201.515 se1 101.959 n1 se2 376.533 se3 108.42 se4 23.7155 sn 201.523 se1 101.353 n2 se2 376.722 se3 108.631 fv37x se4 23.1549 sn 32.2425 se1 78.9637 n3 se2 376.312 se3 108.143 se4 8.24009 sn 32.2437 se1 78.7221 n4 se2 376.335 se3 108.178 se4 9.07417 0 s 0 sn 201.515 se1 101.959 n1 se2 377.062 se3 107.658 se4 24.2668 sn 201.523 se1 101.353 n2 se2 377.263 se3 107.88 fv37y se4 24.5694 sn 32.2425 se1 78.9637 n3 se2 376.867 se3 107.384

bias 13.13517 9.781158 18.14251 11.2435 3.286704 5.269569 8.604157 18.12177 11.21172 1.598847 5.25407 8.594216 18.12196 11.21366 1.54124 0 13.17006 7.787199 10.95351 7.297934 3.817149 13.13424 7.759964 10.96744 7.313579 3.762939 5.268025 6.507736 10.93927 7.279051 2.197532 5.253695 6.497748 10.94135 7.281632 2.243901 0 13.17006 7.787199 10.96092 7.275289 3.78511 13.13424 7.759964 10.97506 7.290925 3.758125 5.268025 6.507736 10.94558 7.257015


300


signal noise trial var se4 8.72419 sn 32.2437 se1 78.7221 n4 se2 376.895 se3 107.423 se4 7.71061 0 s 0 sn 201.74 se1 61.9221 n1 se2 225.439 se3 60.5957 se4 19.1426 sn 201.699 se1 61.6772 n2 se2 225.628 se3 60.8004 fv43y se4 18.0052 sn 32.2785 se1 40.0552 n3 se2 225.253 se3 60.3399 se4 4.37899 sn 32.2718 se1 39.9551 n4 se2 225.276 se3 60.3717 se4 4.18608 0 s 0 sn 201.689 se1 90.546 n1 se2 740.567 se3 204.487 se4 19.8675 sn 201.683 se1 90.4675 n2 se2 740.742 se3 204.694 fv44y se4 18.8598 sn 32.2702 se1 68.92 n3 se2 740.404 se3 204.226 se4 5.36098 sn 32.2693 se1 68.8878 n4 se2 740.422 se3 204.259 se4 5.42063 0 s 0 sn 201.536 se1 201.659

bias 2.116681 5.253695 6.497748 10.94773 7.259817 1.97035 0 13.17958 6.193264 8.211768 5.310673 3.418625 13.14155 6.161042 8.231425 5.333311 3.31697 5.271833 4.763048 8.188717 5.281372 1.616266 5.256621 4.753352 8.19104 5.285123 1.586564 0 13.17754 7.306805 15.25811 8.744981 3.478276 13.14053 7.292309 15.26851 8.762476 3.384414 5.271018 6.038803 15.24753 8.722999 1.801065 5.256211 6.035024 15.24908 8.725963 1.802644 0 13.17031 9.279517


301


signal noise trial var n1 se2 1202.96 se3 345.266 se4 19.3784 sn 201.641 se1 200.926 n2 se2 1203.09 se3 345.498 fv46y se4 17.5175 sn 32.2457 se1 179.482 n3 se2 1202.9 se3 344.953 se4 4.54359 sn 32.2626 se1 179.191 n4 se2 1202.89 se3 344.997 se4 4.20491

bias 17.33643 10.63243 3.386312 13.13908 9.296885 17.34602 10.65298 3.237382 5.268123 8.004946 17.33006 10.60589 1.596562 5.255633 8.016524 17.32984 10.61006 1.555896

niso QRSd LASd RMS40 Comments 1.317 169 59 6.2854 4.435 93 43 7.0635 1.123 90 46 7.0611 1.393 88 44 7.0991 4.928 133 42 7.2733 1.318 169 59 6.2877 4.432 93 43 7.0615 1.114 90 46 7.0464 1.172 89 45 6.9662 4.188 93 43 7.1459 1.315 169 59 6.2871 4.431 92 43 7.0695 1.066 90 46 7.0494 1.165 89 45 7.0039 4.385 134 43 7.1524 1.315 169 59 6.288 4.43 92 43 7.0687 1.065 90 46 7.0425

302

Appendix G. QRS detection evaluation. Influence of noise and interference

noise algorithm results Y fp29 X fp17 Y fv17 Y fp09 Y fp32 Z fp44 X fv17 Y fv23 X fv49 Z fv16 Z fp53 Y fp25 X fp09b X fp18 Z fp10b X fp42 X fv07 Y fv49b X fv23 X fv01b X fp34 Z fp55 Z fp56 Z fv24 Z fv23 Z fv09 Z fp24 X fp50b Z fv01b Z fp09b Z fv20 Z fp52 Z fv17 Z fp58 Z fp06 Z fv05b Z fp31 Y fp50b Z fv57 Z fp60 X fv18 Z fp26 Z fv45 Z fp34 Z fp32 Ave.

n1,3 both SNR 21.3 22 23 23.3 23.4 23.8 24 24.5 25.2 25.2 25.8 26.3 26.6 27 27 27.5 28 28.3 29.1 29.7 30.6 30.7 30.7 31 31.4 31.5 31.6 31.9 32.1 32.6 33 33.3 33.5 33.6 33.7 33.8 34.2 34.4 34.4 34.6 35 35.1 35.3 35.9 36.1 25.6

n2,4 both SNR 13.5 14.2 15.2 15.5 15.6 16 16.2 16.7 17.4 17.4 18 18.5 18.8 19.2 19.2 19.7 20.2 20.5 21.3 21.9 22.8 22.9 22.9 23.2 23.6 23.7 23.8 24.1 24.3 24.8 25.2 25.5 25.7 25.8 25.9 26 26.4 26.6 26.6 26.8 27.2 27.3 27.5 28.1 28.3 17.8

0 mdl N 328 326 328 339 400 258 266 266 385 357 362 349 346 402 346 321 315 329 329 375 258 292 280 329 404 303 292 328 348 309 266 244 315 281 396 375 462 245 299 379 289 342 372 400 435 320

n1 mdl cca N std N std 327 0.5 327 0.16 325 0.19 325 0.19 327 0.33 327 0.33 338 0.19 338 0.19 389 0.61 389 0 257 0.54 257 0 263 0.45 263 0.33 263 0.45 263 0.33 380 0.66 365 0.12 356 0.52 356 0.17 245 0.29 243 0.13 314 0.1 314 0.1 333 0.27 331 0.25 401 0.43 401 0.22 333 0.27 331 0.25 320 0.38 320 0.15 314 0.47 314 0.13 328 0.52 328 0 328 0.52 328 0 374 0.17 374 0.17 257 0.54 257 0 291 0.35 291 0.26 275 0.43 275 0.27 328 0.52 328 0 361 0.6 361 0.05 302 0.28 302 0.14 283 0.41 283 0.28 327 0.33 327 0.33 347 0.34 347 0.34 308 0.51 308 0 263 0.45 263 0.33 243 0.16 243 0.16 314 0.27 314 0.26 280 0.25 280 0.19 395 0.7 387 0.46 374 0.17 374 0.17 299 0.55 299 0.42 244 0.24 244 0.24 298 0.16 298 0.16 378 0.24 378 0.18 288 0.2 288 0.2 341 0.27 341 0.21 367 0.48 361 0.18 389 0.61 389 0 434 0.39 434 0.39 326 0.39 325 0.16

303

n2 mdl cca N std N std 327 0.49 327 0.16 325 0.28 325 0.28 327 0.47 327 0.47 338 0.26 338 0.26 389 0.62 376 0.47 257 0.54 257 0.09 263 0.42 257 0.34 263 0.42 257 0.34 380 0.64 362 0.49 356 0.53 356 0.17 245 0.32 168 0.42 314 0.17 314 0.17 333 0.36 331 0.34 401 0.46 401 0.16 333 0.36 331 0.34 320 0.4 320 0.18 314 0.5 314 0.18 328 0.55 328 0 328 0.55 328 0 374 0.25 374 0.24 257 0.54 257 0.09 291 0.41 291 0.35 275 0.45 233 0.39 328 0.55 328 0 361 0.61 359 0.13 302 0.33 302 0.22 283 0.51 278 0.44 327 0.47 327 0.47 347 0.49 309 0.47 308 0.52 308 0 263 0.42 257 0.34 243 0.24 243 0.24 314 0.36 314 0.36 280 0.32 280 0.27 395 0.7 371 0.49 374 0.25 374 0.24 299 0.55 299 0.42 244 0.4 244 0.4 298 0.23 298 0.23 378 0.28 378 0.29 288 0.35 288 0.35 341 0.32 341 0.29 367 0.51 288 0.49 389 0.62 376 0.47 434 0.5 303 0.46 326 0.43 320 0.26

n3 mdl cca N std N std 327 0.5 327 0.44 325 0.25 325 0.25 327 0.48 327 0.48 338 0.24 338 0.24 389 0.61 383 0.28 257 0.54 257 0.46 263 0.44 263 0.5 263 0.44 263 0.5 380 0.66 376 0.19 356 0.52 356 0.45 245 0.29 238 0.13 314 0.06 314 0.06 333 0.28 331 0.26 401 0.44 401 0.32 333 0.28 331 0.26 320 0.37 320 0.44 314 0.5 314 0.29 328 0.51 328 0.33 328 0.51 328 0.33 374 0.18 374 0.17 257 0.54 257 0.46 291 0.35 291 0.28 275 0.45 275 0.38 328 0.51 328 0.33 361 0.61 359 0.18 302 0.29 302 0.16 283 0.52 281 0.47 327 0.48 327 0.48 347 0.43 347 0.43 308 0.5 306 0.52 263 0.44 263 0.5 243 0.26 243 0.26 314 0.34 314 0.34 280 0.25 280 0.2 395 0.72 381 0.6 374 0.18 374 0.17 299 0.56 299 0.12 244 0.35 244 0.35 298 0.17 298 0.17 378 0.21 378 0.17 288 0.35 288 0.35 341 0.24 341 0.19 367 0.5 365 0.3 389 0.61 383 0.28 434 0.49 434 0.49 326 0.41 325 0.32



n1,3 both SNR 21.3 22 23 23.3 23.4 23.8 24 24.5 25.2 25.2 25.8 26.3 26.6 27 27 27.5 28 28.3 29.1 29.7 30.6 30.7 30.7 31 31.4 31.5 31.6 31.9 32.1 32.6 33 33.3 33.5 33.6 33.7 33.8 34.2 34.4 34.4 34.6 35 35.1 35.3 35.9 36.1 25.6

n2,4 both SNR 13.5 14.2 15.2 15.5 15.6 16 16.2 16.7 17.4 17.4 18 18.5 18.8 19.2 19.2 19.7 20.2 20.5 21.3 21.9 22.8 22.9 22.9 23.2 23.6 23.7 23.8 24.1 24.3 24.8 25.2 25.5 25.7 25.8 25.9 26 26.4 26.6 26.6 26.8 27.2 27.3 27.5 28.1 28.3 17.8

0 mdl N 328 326 328 339 400 258 266 266 385 357 362 349 346 402 346 321 315 329 329 375 258 292 280 329 404 303 292 328 348 309 266 244 315 281 396 375 462 245 299 379 289 342 372 400 435 320


304

Comments



n1,3 both SNR 21.3 22 23 23.3 23.4 23.8 24 24.5 25.2 25.2 25.8 26.3 26.6 27 27 27.5 28 28.3 29.1 29.7 30.6 30.7 30.7 31 31.4 31.5 31.6 31.9 32.1 32.6 33 33.3 33.5 33.6 33.7 33.8 34.2 34.4 34.4 34.6 35 35.1 35.3 35.9 36.1 25.6

n2,4 both SNR 13.5 14.2 15.2 15.5 15.6 16 16.2 16.7 17.4 17.4 18 18.5 18.8 19.2 19.2 19.7 20.2 20.5 21.3 21.9 22.8 22.9 22.9 23.2 23.6 23.7 23.8 24.1 24.3 24.8 25.2 25.5 25.7 25.8 25.9 26 26.4 26.6 26.6 26.8 27.2 27.3 27.5 28.1 28.3 17.8

0 mdl N 328 326 328 339 400 258 266 266 385 357 362 349 346 402 346 321 315 329 329 375 258 292 280 329 404 303 292 328 348 309 266 244 315 281 396 375 462 245 299 379 289 342 372 400 435 320

n1 mdl cca N std N std 327 0.5 327 0.16 325 0.19 325 0.19 327 0.33 327 0.33 338 0.19 338 0.19 389 0.61 389 0 257 0.54 257 0 263 0.45 263 0.33 263 0.45 263 0.33 380 0.66 365 0.12 356 0.52 356 0.17 245 0.29 243 0.13 314 0.1 314 0.1 333 0.27 331 0.25 401 0.43 401 0.22 333 0.27 331 0.25 320 0.38 320 0.15 314 0.47 314 0.13 328 0.52 328 0 328 0.52 328 0 374 0.17 374 0.17 257 0.54 257 0 291 0.35 291 0.26 275 0.43 275 0.27 328 0.52 328 0 361 0.6 361 0.05 302 0.28 302 0.14 283 0.41 283 0.28 327 0.33 327 0.33 347 0.34 347 0.34 308 0.51 308 0 263 0.45 263 0.33 243 0.16 243 0.16 314 0.27 314 0.26 280 0.25 280 0.19 395 0.7 387 0.46 374 0.17 374 0.17 299 0.55 299 0.42 244 0.24 244 0.24 298 0.16 298 0.16 378 0.24 378 0.18 288 0.2 288 0.2 341 0.27 341 0.21 367 0.48 361 0.18 389 0.61 389 0 434 0.39 434 0.39 326 0.39 325 0.16

303

n2 mdl cca N std N std 327 0.49 327 0.16 325 0.28 325 0.28 327 0.47 327 0.47 338 0.26 338 0.26 389 0.62 376 0.47 257 0.54 257 0.09 263 0.42 257 0.34 263 0.42 257 0.34 380 0.64 362 0.49 356 0.53 356 0.17 245 0.32 168 0.42 314 0.17 314 0.17 333 0.36 331 0.34 401 0.46 401 0.16 333 0.36 331 0.34 320 0.4 320 0.18 314 0.5 314 0.18 328 0.55 328 0 328 0.55 328 0 374 0.25 374 0.24 257 0.54 257 0.09 291 0.41 291 0.35 275 0.45 233 0.39 328 0.55 328 0 361 0.61 359 0.13 302 0.33 302 0.22 283 0.51 278 0.44 327 0.47 327 0.47 347 0.49 309 0.47 308 0.52 308 0 263 0.42 257 0.34 243 0.24 243 0.24 314 0.36 314 0.36 280 0.32 280 0.27 395 0.7 371 0.49 374 0.25 374 0.24 299 0.55 299 0.42 244 0.4 244 0.4 298 0.23 298 0.23 378 0.28 378 0.29 288 0.35 288 0.35 341 0.32 341 0.29 367 0.51 288 0.49 389 0.62 376 0.47 434 0.5 303 0.46 326 0.43 320 0.26




n1,3 both SNR 21.3 22 23 23.3 23.4 23.8 24 24.5 25.2 25.2 25.8 26.3 26.6 27 27 27.5 28 28.3 29.1 29.7 30.6 30.7 30.7 31 31.4 31.5 31.6 31.9 32.1 32.6 33 33.3 33.5 33.6 33.7 33.8 34.2 34.4 34.4 34.6 35 35.1 35.3 35.9 36.1 25.6

n2,4 both SNR 13.5 14.2 15.2 15.5 15.6 16 16.2 16.7 17.4 17.4 18 18.5 18.8 19.2 19.2 19.7 20.2 20.5 21.3 21.9 22.8 22.9 22.9 23.2 23.6 23.7 23.8 24.1 24.3 24.8 25.2 25.5 25.7 25.8 25.9 26 26.4 26.6 26.6 26.8 27.2 27.3 27.5 28.1 28.3 17.8

0 mdl N 328 326 328 339 400 258 266 266 385 357 362 349 346 402 346 321 315 329 329 375 258 292 280 329 404 303 292 328 348 309 266 244 315 281 396 375 462 245 299 379 289 342 372 400 435 320


304

Comments

Appendix H. QRS detection evaluation. Enhanced double-level algorithm

ID p06 p07 p09 p13 p15b p16 p17 p18b p21 p24 p29 p30 p32 p38 p38b p40 p41 p42 p49 p51 p53 p54b p57 p57b p58 p62 v01 v02 v02b v03 v04b v05 v05b v06 v07 v08 v09 v10 v11 v12 v13 v14 v15 v16 v16b v17 v19 v21 v23 v24

SNR X 31 22.2 28.3 26.7 20.8 31.2 26.7 11 23.9 26.8 16.8 28 21.8 26.6 26 15 22.5 31.5 12.6 32.5 28 28.3 20.6 20.2 26.9 26.1 25.8 26.9 28.2 26.6 20.6 23.5 20.1 29.1 25.6 28.6 29.9 24.9 25.8 29.7 28.1 23 27.7 25.2 27 22.1 29.4 24.8 33.3 20.2

SNR Y 25.6 31.9 26.2 28.3 24.9 19.5 22.2 22 10.1 20.9 12.9 24.7 24.1 19.7 19.7 18.7 27.6 28.8 12.1 30.9 21.7 18.1 13.2 12.7 17.6 21.3 26 16.6 16.3 22.5 23.8 23.6 22.9 27.1 20.9 26 13.7 21.2 17.3 20.6 25.1 18.7 15.4 12.1 17.3 22.7 25.7 22.1 28 23.8

SNR Nmin Z 25 307 40.8 388 29.5 336 30.2 167 27 391 28 394 36.1 297 24.6 55 26.9 126 34.4 297 13.4 327 27.9 367 41.9 399 31.8 315 32.2 244 26.7 312 30.4 266 34.1 318 21.9 100 41.8 485 31.1 291 32.1 121 32.4 144 38 252 36.5 370 22.2 218 35.4 383 34.5 217 33.7 224 32.6 288 34.6 290 38.9 299 39.4 300 38.6 275 34 314 29.5 293 30.9 354 29.3 319 25 272 35.4 320 35.8 376 27.9 430 26.8 227 16.2 300 22.2 297 38.9 209 36.4 403 33.6 277 36.8 324 35.3 367

std XY 0.72 0.86 0.72 1.1 1.38 0.89 1.03 0.52 0.7 0.79 0.63 0.71 0.65 0.63 0.56 0.56 0.71 0.49 0.81 0.73 0.7 0.63 0.55 0.63 0.79 0.52 0.55 1.07 0.68 0.89 0.91 0.55 0.61 0.77 0.56 0.92 0.61 0.87 0.81 0.84 0.69 0.83 0.49 0.85 1.2 0.57 0.75 0.52 0.57 1.03

std XZ 0.62 0.88 0.68 0.97 1.49 0.85 1.05 0.4 0.76 0.9 0.6 0.5 0.6 0.48 0.37 0.9 0.58 0.54 0.69 0.73 0.65 0.71 0.48 0.54 0.8 1.28 0.64 1.07 0.53 0.82 0.8 0.7 0.76 0.5 0.69 0.92 0.63 0.72 0.63 0.69 1.09 0.9 0.55 0.74 0.92 0.79 0.69 1.07 0.71 0.71

std XC 0.62 0.96 0.52 1.04 1.25 0.54 1.37 0.55 0.57 0.72 0.65 0.45 0.76 0.51 0.51 0.68 0.73 0.77 0.59 0.5 0.91 0.73 0.52 0.58 0.7 0.43 0.74 0.8 0.71 0.63 0.69 0.87 0.76 0.54 0.64 0.66 0.63 0.59 0.63 0.71 0.85 0.4 0.52 0.7 1.05 0.73 0.67 0.67 0.51 0.92

305

std YZ 0.67 0.5 0.91 0.8 0.9 0.82 0.7 0.5 0.54 0.68 0.66 0.73 0.75 0.68 0.65 0.77 0.58 0.52 0.56 0.54 0.6 0.73 0.54 0.65 0.74 1.26 0.52 0.49 0.69 0.73 0.69 0.63 0.63 0.84 0.74 0.78 0.59 1.01 1 0.65 0.79 0.66 0.68 0.95 0.73 0.77 0.94 1.02 0.69 0.6

std YC 0.89 0.69 0.73 0.88 0.79 0.94 0.77 0.48 0.39 0.59 0.62 0.64 0.72 0.73 0.52 0.73 0.67 0.68 0.55 0.64 0.76 0.55 0.6 0.84 0.99 0.56 0.59 0.58 0.61 0.61 0.75 0.64 1.01 0.51 0.65 0.69 0.72 1.16 0.99 0.69 0.83 0.79 0.68 1.03 0.57 0.71 0.83 0.51 0.58 0.56

std ZC 0.53 0.65 0.5 0.35 0.84 0.77 0.73 0.47 0.52 0.79 0.62 0.53 0.68 0.65 0.57 1.23 0.57 0.85 0.5 0.66 0.83 0.53 0.53 0.77 0.96 1.19 0.65 0.64 0.75 0.74 0.64 0.71 1.04 0.61 0.65 0.73 0.76 0.66 0.56 0.45 1.02 0.91 0.64 0.58 0.55 0.71 0.67 0.9 0.74 0.55

std X 0.42 0.79 0.39 0.91 1.24 0.49 1.04 0.36 0.59 0.64 0.44 0.34 0.44 0.25 0.26 0.3 0.52 0.36 0.59 0.5 0.56 0.54 0.34 0.24 0.42 0.37 0.5 0.9 0.43 0.62 0.64 0.55 0.3 0.4 0.41 0.66 0.38 0.28 0.31 0.62 0.64 0.49 0.23 0.46 0.97 0.48 0.39 0.52 0.37 0.8

std Y 0.64 0.36 0.68 0.72 0.6 0.72 0.36 0.37 0.34 0.39 0.46 0.6 0.52 0.56 0.47 0.13 0.48 0.24 0.5 0.46 0.39 0.43 0.44 0.55 0.61 0.43 0.28 0.46 0.46 0.55 0.6 0.28 0.47 0.61 0.46 0.59 0.43 0.91 0.84 0.58 0.32 0.53 0.47 0.82 0.63 0.44 0.7 0.35 0.4 0.55

std Z 0.29 0.35 0.54 0.24 0.75 0.58 0.34 0.28 0.47 0.62 0.44 0.41 0.45 0.41 0.39 0.87 0.29 0.46 0.36 0.47 0.41 0.49 0.34 0.45 0.59 1.19 0.41 0.49 0.47 0.57 0.44 0.46 0.6 0.5 0.54 0.61 0.47 0.5 0.48 0.3 0.8 0.67 0.47 0.47 0.3 0.59 0.57 0.91 0.59 0.13

std C 0.52 0.56 0.22 0.44 0.38 0.48 0.75 0.37 0.15 0.43 0.45 0.29 0.55 0.47 0.37 0.74 0.49 0.68 0.25 0.37 0.7 0.36 0.41 0.6 0.71 0.24 0.52 0.2 0.53 0.33 0.4 0.6 0.82 0.21 0.44 0.32 0.56 0.57 0.47 0.35 0.66 0.46 0.46 0.51 0.33 0.5 0.46 0.32 0.4 0.4


SNR X v25 32.7 v26 30 v27 35.8 v28 25.7 v30 30.1 v32b 24.1 v33 29.9 v34 25.8 v35 24.3 v37 21.5 v38 25.8 v39 23.4 v40 29 v41 23.2 v42 34.4 v43 20.8 v44 28.1 v45 33.2 v48 29.7 v49 26.9 v49b 25.7 v50 27.9 v51 32.1 v54 32.3 v55 29.7 v56 31.3 v58 31 v59 28.9 v61 30.8 v63 28.8 Ave. 26.4 ID

SNR Y 25.9 15.2 26.4 29.7 28.7 25.6 26.2 21.5 16.9 15.8 24.7 27.7 25.3 26 26.2 27 25.8 24.4 21.3 29.9 30.6 30.8 32 16.4 30 29.8 20.8 31.2 20.2 23.8 22.8

SNR Nmin Z 32.4 329 27.4 247 30.2 293 25.7 292 35.5 373 34.5 322 32.6 287 28.6 310 23.8 332 29.6 238 27.3 186 32.1 409 31.5 307 26.7 362 33.7 250 31.7 310 22.5 342 33.6 275 31.7 511 29.8 384 24.4 395 32.9 411 32.6 374 32.6 177 28.8 519 33.3 380 31.4 65 30.8 326 34.3 292 29 380 31.1 304

std XY 0.7 0.82 1 0.64 0.73 1.07 0.92 0.71 0.72 0.68 1.15 0.61 0.88 0.67 0.58 0.8 0.63 0.8 1.57 0.62 0.72 0.77 1.03 0.72 0.65 0.86 0.73 0.89 0.73 0.72 0.77

std XZ 0.64 0.76 1.18 0.75 0.96 0.91 0.95 0.74 0.65 0.68 1.13 0.89 0.83 0.66 0.74 0.66 0.9 0.79 0.87 0.66 0.72 0.56 0.75 0.57 0.55 1.23 0.51 0.92 0.78 0.54 0.76

std XC 0.66 0.51 0.89 0.69 0.6 1 0.9 0.84 0.62 0.69 0.81 0.78 1.04 0.58 0.69 0.84 0.94 0.71 1.16 0.54 0.99 0.78 0.55 0.45 0.54 0.85 0.61 0.47 0.7 0.6 0.71

306

std YZ 1.03 0.58 0.9 0.62 0.6 0.7 0.44 0.85 0.75 0.65 0.55 0.69 0.83 0.6 0.79 0.74 0.82 0.65 1.09 0.88 0.54 0.91 0.64 0.66 0.5 0.71 0.73 0.62 0.7 0.73 0.72

std YC 0.69 0.82 0.66 0.55 0.64 0.79 0.38 0.97 0.78 0.76 0.73 0.58 0.64 0.6 0.55 0.56 0.87 0.74 0.74 0.56 0.58 0.68 1.13 0.85 0.41 0.58 0.43 0.81 0.78 0.67 0.7

std ZC 0.93 0.74 0.82 0.51 0.72 0.68 0.44 0.74 0.72 0.4 0.73 0.74 0.83 0.66 0.66 0.71 0.92 0.57 0.63 0.69 0.68 0.94 0.74 0.65 0.52 0.7 0.55 0.83 0.56 0.58 0.69

std X 0.2 0.5 0.86 0.57 0.63 0.86 0.88 0.46 0.4 0.52 0.93 0.61 0.74 0.46 0.48 0.61 0.56 0.61 1.08 0.33 0.7 0.38 0.52 0.29 0.47 0.88 0.47 0.57 0.55 0.42 0.54

std Y 0.63 0.58 0.53 0.39 0.37 0.61 0.28 0.65 0.59 0.55 0.56 0.26 0.46 0.43 0.43 0.47 0.43 0.54 0.99 0.54 0.23 0.57 0.82 0.63 0.37 0.27 0.51 0.56 0.56 0.58 0.51

std Z 0.74 0.47 0.77 0.46 0.62 0.36 0.36 0.5 0.5 0.31 0.53 0.62 0.56 0.47 0.59 0.47 0.66 0.42 0.24 0.63 0.35 0.63 0.25 0.39 0.36 0.73 0.43 0.6 0.45 0.41 0.5

std C 0.52 0.48 0.31 0.35 0.36 0.54 0.23 0.66 0.5 0.42 0.3 0.48 0.61 0.41 0.39 0.48 0.72 0.43 0.17 0.31 0.6 0.6 0.61 0.48 0.28 0.24 0.25 0.43 0.45 0.4 0.45


ID fp06 fp07 fp09 fp13 fp15b fp16 fp17 fp18b fp21 fp24 fp29 fp30 fp32 fp38 fp38b fp40 fp41 fp42 fp49 fp51 fp53 fp54b fp57 fp57b fp58 fp62 fv01 fv02 fv02b fv03 fv04b fv05 fv05b fv06 fv07 fv08 fv09 fv10 fv11 fv12 fv13 fv14 fv15 fv16 fv16b fv17 fv19 fv21 fv23 fv24

SNR X 32.8 31.3 28.9 30.6 21.7 32.9 38.5 28.4 24.4 26.9 25.2 28.5 30.2 30.7 30.5 15.1 23 32.4 14.2 38.6 31.5 28.2 20.6 23.3 33.4 28.4 34.6 33.2 35.7 35.9 28.7 28.6 24 37 35.2 31.5 33.5 29 25.9 34.6 29.7 25.3 30.1 28.2 27.8 34.3 33.6 26 38.4 23.5

SNR Y 32.5 33.3 28.1 29.2 25.2 20.5 34.3 34.2 14.7 21.2 28.4 25 32 20.2 21 19.1 27.8 29.7 12.1 32.9 26.1 21.1 14.7 14.8 25.7 23.4 33.9 24.7 25.6 34.3 28.1 28.2 24.7 29.9 26.8 30.4 15.3 25 20.6 28.4 31.3 22.7 17.3 20.5 23.6 34.4 33.6 27 35 30.6

SNR Nmin Z 40.6 307 42.1 401 35.3 336 42.2 165 28.3 393 27.8 398 40.3 303 41.9 278 28 183 35.9 299 30.9 327 28.1 367 43.4 399 36.1 315 34.1 244 27 316 30.8 266 34.5 318 24.2 132 45.1 485 35 291 33.4 107 35.7 151 38.7 306 40.7 376 23.9 218 40.7 383 38.8 224 41.4 231 35.6 288 40.9 288 41.6 299 39.7 300 42.2 275 40.4 314 30.6 291 34 356 29.9 319 24.4 272 40.6 320 36.1 376 28.4 430 27 233 29 312 27.1 297 46.9 209 37.4 405 39.6 277 42.4 324 37.5 367

std XY 0.71 0.84 0.72 1.11 1.31 0.88 1.02 0.57 0.73 0.79 0.6 0.72 0.74 0.63 0.56 0.58 0.7 0.5 0.86 0.73 0.69 0.77 0.56 0.78 0.8 0.52 0.54 1.12 0.72 0.9 0.91 0.55 0.62 0.77 0.56 0.92 0.6 0.87 0.81 0.84 0.73 0.82 0.44 0.87 1.2 0.57 0.75 0.43 0.58 1.03

std XZ 0.62 0.89 0.6 0.95 1.49 0.85 1.19 0.47 0.64 0.92 0.59 0.51 0.6 0.48 0.37 0.84 0.57 0.56 0.67 0.73 0.65 0.71 0.5 0.62 0.8 1.28 0.64 0.89 0.61 0.81 0.8 0.9 0.76 0.5 0.69 0.92 0.63 0.72 0.63 0.69 1.12 0.9 0.55 0.73 0.92 0.79 0.7 1.15 0.7 0.67

std XC 0.62 0.91 0.55 0.87 1.24 0.54 1.36 0.61 0.6 0.72 0.8 0.46 0.76 0.51 0.51 0.75 0.8 0.77 0.69 0.5 0.91 0.68 0.65 0.65 0.49 0.43 0.74 0.54 0.5 0.52 0.69 0.87 0.75 0.54 0.64 0.66 0.62 0.59 0.63 0.71 0.84 0.4 0.88 0.7 1.05 0.73 0.69 0.54 0.51 0.94

307

std YZ 0.67 0.5 0.89 0.8 0.91 0.83 0.73 0.54 0.45 0.68 0.6 0.73 0.76 0.68 0.65 0.78 0.58 0.55 0.69 0.54 0.59 0.79 0.54 0.69 0.74 1.26 0.51 0.6 0.57 0.72 0.68 0.69 0.63 0.84 0.74 0.77 0.59 1.01 1 0.65 0.83 0.65 0.63 0.93 0.73 0.78 0.7 1.08 0.72 0.67

std YC 0.9 0.71 0.75 0.87 0.84 0.95 0.77 0.56 0.88 0.59 0.79 0.64 0.67 0.73 0.52 0.73 0.67 0.69 1 0.64 0.77 0.58 0.61 0.96 0.72 0.56 0.61 0.81 0.67 0.77 0.74 0.64 1.07 0.51 0.65 0.69 0.74 1.16 1 0.69 0.81 0.82 0.92 1.05 0.57 0.72 0.85 0.44 0.56 0.55

std ZC 0.53 0.66 0.54 0.41 0.84 0.77 0.53 0.57 0.84 0.79 0.62 0.53 0.68 0.65 0.57 1.23 0.57 0.92 0.63 0.66 0.83 0.47 0.65 0.73 0.63 1.19 0.65 0.65 0.59 0.66 0.64 0.5 1.05 0.61 0.65 0.71 0.76 0.66 0.55 0.45 1.02 0.93 0.9 0.57 0.55 0.71 0.82 0.96 0.77 0.61

std X 0.41 0.76 0.34 0.84 1.21 0.48 1.1 0.39 0.39 0.65 0.47 0.35 0.49 0.25 0.26 0.3 0.55 0.34 0.49 0.5 0.56 0.57 0.39 0.4 0.52 0.37 0.49 0.73 0.44 0.56 0.64 0.66 0.27 0.4 0.41 0.66 0.37 0.27 0.31 0.62 0.66 0.47 0.29 0.46 0.97 0.48 0.44 0.47 0.35 0.78

std Y 0.64 0.37 0.69 0.76 0.59 0.72 0.36 0.4 0.5 0.39 0.46 0.6 0.54 0.56 0.47 0.18 0.46 0.23 0.72 0.46 0.38 0.57 0.38 0.67 0.6 0.43 0.29 0.71 0.52 0.64 0.6 0.31 0.51 0.61 0.46 0.59 0.44 0.91 0.84 0.58 0.35 0.53 0.41 0.82 0.63 0.45 0.56 0.3 0.41 0.57

std Z 0.3 0.39 0.5 0.34 0.77 0.59 0.4 0.33 0.4 0.63 0.32 0.41 0.46 0.42 0.39 0.84 0.26 0.52 0.26 0.47 0.41 0.46 0.36 0.37 0.54 1.19 0.4 0.4 0.38 0.5 0.44 0.52 0.59 0.5 0.54 0.6 0.47 0.5 0.48 0.3 0.83 0.67 0.45 0.43 0.3 0.59 0.51 1.02 0.62 0.22

std C 0.52 0.55 0.32 0.31 0.43 0.48 0.65 0.45 0.65 0.42 0.61 0.29 0.5 0.47 0.37 0.77 0.52 0.7 0.59 0.37 0.7 0.23 0.51 0.62 0.28 0.24 0.53 0.23 0.38 0.32 0.39 0.45 0.84 0.21 0.44 0.31 0.57 0.57 0.48 0.35 0.62 0.49 0.81 0.53 0.33 0.5 0.6 0.14 0.4 0.44


SNR X fv25 34.9 fv26 33.7 fv27 40.3 fv28 30.1 fv30 32 fv32b 23.3 fv33 30.8 fv34 28.2 fv35 25.6 fv37 22.1 fv38 27.4 fv39 25.8 fv40 31 fv41 27.3 fv42 36.2 fv43 29.1 fv44 29.2 fv45 37.6 fv48 30.5 fv49 30 fv49b 29 fv50 29 fv51 34.8 fv54 33.3 fv55 30.9 fv56 33.9 fv58 33.4 fv59 35.8 fv61 32.4 fv63 29.6 Ave. 30 ID

SNR Y 26.3 17.1 27.7 32.6 30.7 25.9 28.4 22 17.1 18.1 27.3 27.3 27.2 28.1 27.2 29.1 25.9 25 25.1 31.9 32 30.9 32.7 15.8 31 32.7 21.2 33.3 25.1 24.5 26.2

SNR Nmin Z 37 329 28.8 247 31.2 293 34 292 38 375 35.9 306 35.7 287 30.7 310 24.7 328 30.4 274 31.9 188 34.5 409 37.1 309 34.8 364 36.3 252 33.4 310 24.3 342 40.5 275 33.3 513 32.8 384 25.9 395 38.1 411 37.3 374 36.4 176 33.8 519 37.4 382 38.3 124 37.5 326 38 292 37 382 35 310

std XY 0.74 0.65 1 0.53 0.58 1.13 0.6 0.65 0.7 1.03 1.29 0.68 0.57 0.65 0.57 0.85 0.65 0.81 1.31 0.6 0.58 0.61 1.17 0.75 0.58 0.83 0.7 0.86 0.66 0.55 0.76

std XZ 0.58 0.69 1.22 0.7 0.94 0.89 0.58 0.76 0.89 0.8 1.07 0.86 0.7 0.69 0.66 0.77 0.89 0.79 0.91 0.69 0.95 0.67 0.69 0.58 0.55 1.28 0.69 0.94 0.77 0.53 0.77

std XC 0.77 0.5 0.89 0.69 0.58 0.92 0.53 0.52 0.61 0.62 0.81 0.8 0.65 0.48 0.64 1.16 0.9 0.71 1.01 0.55 0.66 0.68 0.55 0.46 0.54 0.57 0.94 0.51 0.69 0.57 0.69

308

std YZ 0.94 0.64 0.87 0.73 0.73 0.64 0.66 0.83 0.85 0.57 0.6 0.64 0.84 0.65 0.56 0.54 0.77 0.62 1.34 0.89 0.74 0.67 0.88 0.74 0.5 1 0.49 0.62 0.58 0.61 0.72

std YC 0.7 0.63 0.68 0.72 0.51 0.77 0.68 0.62 0.79 0.91 0.74 0.51 0.64 0.56 0.57 0.56 0.51 0.74 0.96 0.57 0.57 0.91 1.21 0.92 0.41 0.74 0.63 0.62 0.56 0.72 0.72

std ZC 0.88 0.7 0.86 0.53 0.92 0.62 0.38 0.6 1.05 0.61 0.65 0.6 0.84 0.66 0.39 0.71 0.92 0.58 0.68 0.63 1.02 1.04 0.64 0.7 0.52 1 0.71 0.8 0.57 0.58 0.7

std X 0.36 0.41 0.88 0.44 0.5 0.86 0.39 0.43 0.38 0.66 0.96 0.66 0.34 0.43 0.51 0.84 0.63 0.62 0.81 0.36 0.49 0.19 0.53 0.25 0.44 0.68 0.65 0.62 0.58 0.32 0.52

std Y 0.6 0.45 0.49 0.48 0.18 0.65 0.54 0.55 0.48 0.71 0.7 0.3 0.46 0.44 0.39 0.2 0.14 0.54 1.05 0.55 0.11 0.47 1 0.69 0.32 0.5 0.26 0.45 0.36 0.49 0.51

std Z 0.63 0.53 0.79 0.48 0.77 0.27 0.34 0.6 0.79 0.27 0.41 0.53 0.66 0.53 0.35 0.26 0.7 0.41 0.65 0.62 0.8 0.62 0.16 0.43 0.38 0.98 0.34 0.64 0.46 0.37 0.5

std C 0.57 0.4 0.34 0.45 0.43 0.44 0.33 0.25 0.6 0.43 0.14 0.39 0.51 0.33 0.34 0.67 0.58 0.43 0.28 0.26 0.55 0.76 0.54 0.52 0.31 0.27 0.62 0.31 0.38 0.48 0.46

Appendix I. QRS detection evaluation. Cross-correlation adjust

ID p06 p07 p09 p13 p15b p16 p17 p18b p21 p24 p29 p30 p32 p38 p38b p40 p41 p42 p49 p51 p53 p54b p57 p57b p58 p62 v01 v02 v02b v03 v04b v05 v05b v06 v07 v08 v09 v10 v11 v12 v13 v14 v15 v16 v16b v17 v19 v21 v23 v24

SNR X 31 22.2 28.3 26.7 20.8 31.2 26.7 11 23.9 26.8 16.8 28 21.8 26.6 26 15 22.5 31.5 12.6 32.5 28 28.3 20.6 20.2 26.9 26.1 25.8 26.9 28.2 26.6 20.6 23.5 20.1 29.1 25.6 28.6 29.9 24.9 25.8 29.7 28.1 23 27.7 25.2 27 22.1 29.4 24.8 33.3 20.2

SNR Y 25.6 31.9 26.2 28.3 24.9 19.5 22.2 22 10.1 20.9 12.9 24.7 24.1 19.7 19.7 18.7 27.6 28.8 12.1 30.9 21.7 18.1 13.2 12.7 17.6 21.3 26 16.6 16.3 22.5 23.8 23.6 22.9 27.1 20.9 26 13.7 21.2 17.3 20.6 25.1 18.7 15.4 12.1 17.3 22.7 25.7 22.1 28 23.8

SNR Nmin Z 25 308 40.8 597 29.5 338 30.2 620 27 447 28 429 36.1 326 24.6 279 26.9 302 34.4 342 13.4 328 27.9 368 41.9 400 31.8 316 32.2 245 26.7 423 30.4 305 34.1 321 21.9 404 41.8 486 31.1 292 32.1 341 32.4 233 38 442 36.5 379 22.2 232 35.4 384 34.5 388 33.7 390 32.6 301 34.6 345 38.9 300 39.4 303 38.6 276 34 315 29.5 326 30.9 357 29.3 320 25 279 35.4 322 35.8 425 27.9 431 26.8 254 16.2 315 22.2 298 38.9 266 36.4 408 33.6 280 36.8 329 35.3 372

std XY 0.62 1 0.48 1.43 0.84 0.9 0.43 0.63 0.96 0.76 0.49 0.5 0.59 0.59 0.59 0.59 0.6 0.46 1.06 0.47 0.54 1.07 0.83 0.86 0.67 0.56 0.5 0.98 1.05 0.64 1.04 0.49 0.37 0.36 0.47 0.55 0.56 0.56 0.73 0.61 0.9 0.7 0.66 0.74 0.69 0.57 0.48 0.47 0.58 0.6

std XZ 0.53 0.89 0.54 1.07 0.8 0.7 0.7 0.49 0.72 0.83 0.55 0.51 0.52 0.49 0.4 1.06 0.5 0.45 0.79 0.49 0.55 0.64 0.55 0.54 0.53 0.72 0.67 0.39 0.33 0.84 0.83 0.59 0.64 0.52 0.51 0.68 0.42 0.68 0.48 0.5 0.95 0.39 0.5 0.58 0.66 0.91 0.56 0.63 0.59 0.53

std XC 0.47 0.48 0.52 1.11 0.76 0.49 0.58 0.66 0.62 0.68 0.49 0.28 0.51 0.38 0.29 0.6 0.55 0.79 0.63 0.5 0.49 0.51 0.46 0.45 0.39 0.43 0.51 0.56 0.54 0.44 0.69 0.56 0.52 0.44 0.43 0.57 0.49 0.51 0.45 0.45 1.05 0.49 0.55 0.53 0.59 0.49 0.51 0.44 0.39 0.53

309

std YZ 0.51 0.57 0.71 0.85 1.12 0.85 0.77 0.51 0.64 0.52 0.54 0.63 0.62 0.52 0.54 0.98 0.6 0.51 0.84 0.5 0.55 1.36 0.68 0.78 0.51 0.64 0.51 0.86 0.98 0.63 0.69 0.63 0.63 0.52 0.41 0.51 0.53 0.64 0.76 0.53 0.8 0.69 0.81 0.63 0.61 0.86 0.51 0.47 0.64 0.51

std YC 0.5 1.09 0.68 0.84 0.91 0.97 0.64 0.42 0.77 0.44 0.55 0.5 0.58 0.57 0.59 0.55 0.77 0.73 0.88 0.52 0.51 0.98 0.71 0.77 0.55 0.69 0.4 0.76 0.76 0.61 0.77 0.61 0.51 0.48 0.48 0.5 0.52 0.44 0.69 0.48 0.76 0.55 0.66 0.49 0.45 0.5 0.42 0.44 0.48 0.62

std ZC 0.41 0.92 0.24 0.46 0.93 0.75 0.48 0.51 0.51 0.46 0.58 0.5 0.49 0.49 0.36 1.21 0.65 0.92 0.5 0.49 0.58 0.79 0.49 0.48 0.46 0.83 0.46 0.48 0.5 0.81 0.51 0.36 0.38 0.49 0.44 0.5 0.5 0.53 0.51 0.45 0.5 0.54 0.7 0.51 0.5 0.68 0.45 0.5 0.53 0.52

std X 0.43 0.53 0.31 1.1 0.39 0.38 0.36 0.49 0.63 0.68 0.33 0.22 0.36 0.32 0.27 0.4 0.28 0.27 0.65 0.33 0.36 0.17 0.44 0.41 0.41 0.28 0.46 0.47 0.45 0.45 0.73 0.39 0.37 0.27 0.35 0.49 0.33 0.44 0.32 0.4 0.83 0.34 0.26 0.49 0.53 0.47 0.4 0.4 0.35 0.4

std Y 0.43 0.72 0.54 0.85 0.76 0.78 0.47 0.35 0.67 0.35 0.36 0.45 0.48 0.46 0.52 0.2 0.52 0.23 0.81 0.35 0.37 1.05 0.65 0.73 0.48 0.41 0.26 0.8 0.88 0.37 0.69 0.45 0.36 0.31 0.32 0.31 0.42 0.37 0.64 0.43 0.55 0.56 0.58 0.5 0.42 0.43 0.3 0.27 0.44 0.44

std Z 0.3 0.5 0.35 0.17 0.76 0.51 0.53 0.29 0.29 0.43 0.42 0.46 0.37 0.34 0.25 1.01 0.37 0.45 0.38 0.34 0.43 0.75 0.32 0.35 0.32 0.61 0.44 0.25 0.33 0.65 0.34 0.38 0.46 0.41 0.32 0.43 0.32 0.51 0.39 0.33 0.43 0.37 0.52 0.39 0.43 0.73 0.38 0.44 0.48 0.32

std C 0.24 0.63 0.3 0.26 0.57 0.49 0.34 0.37 0.33 0.2 0.39 0.19 0.34 0.3 0.23 0.55 0.52 0.75 0.25 0.36 0.35 0.23 0.28 0.27 0.23 0.49 0.22 0.26 0.11 0.39 0.26 0.33 0.26 0.33 0.31 0.32 0.35 0.21 0.3 0.25 0.5 0.3 0.43 0.22 0.23 0.07 0.28 0.27 0.2 0.4

Appendix I. QRS detection evaluation. Cross-correlation adjust

SNR X v25 32.7 v26 30 v27 35.8 v28 25.7 v30 30.1 v32b 24.1 v33 29.9 v34 25.8 v35 24.3 v37 21.5 v38 25.8 v39 23.4 v40 29 v41 23.2 v42 34.4 v43 20.8 v44 28.1 v45 33.2 v48 29.7 v49 26.9 v49b 25.7 v50 27.9 v51 32.1 v54 32.3 v55 29.7 v56 31.3 v58 31 v59 28.9 v61 30.8 v63 28.8 Ave. 26.4 ID

SNR Y 25.9 15.2 26.4 29.7 28.7 25.6 26.2 21.5 16.9 15.8 24.7 27.7 25.3 26 26.2 27 25.8 24.4 21.3 29.9 30.6 30.8 32 16.4 30 29.8 20.8 31.2 20.2 23.8 22.8

SNR Nmin Z 32.4 330 27.4 264 30.2 294 25.7 293 35.5 380 34.5 339 32.6 326 28.6 313 23.8 359 29.6 326 27.3 458 32.1 410 31.5 310 26.7 367 33.7 255 31.7 311 22.5 343 33.6 299 31.7 514 29.8 385 24.4 396 32.9 412 32.6 378 32.6 349 28.8 520 33.3 389 31.4 430 30.8 327 34.3 295 29 383 31.1 353

std XY 0.63 0.57 0.71 0.56 0.45 0.97 0.49 0.54 0.62 0.71 0.71 0.51 0.48 0.39 0.4 0.37 0.5 0.6 0.49 0.52 0.49 0.7 0.55 0.89 0.46 0.54 0.64 0.52 0.5 0.39 0.63

std XZ 0.46 0.55 0.46 0.5 0.71 0.86 0.38 0.46 0.56 0.61 0.84 0.78 0.74 0.47 0.54 0.55 0.89 0.61 0.55 0.57 0.46 0.51 0.39 0.49 0.4 0.67 0.57 0.68 0.61 0.52 0.6

std XC 0.48 0.5 0.33 0.48 0.5 0.72 0.5 0.32 0.41 0.55 0.62 0.57 0.41 0.47 0.67 0.5 0.44 0.43 0.36 0.52 0.49 0.42 0.49 0.36 0.47 0.5 0.44 0.44 0.62 0.44 0.52

310

std YZ 0.71 0.57 0.69 0.51 0.6 0.53 0.44 0.6 0.57 0.61 0.55 0.58 0.83 0.49 0.52 0.54 0.85 0.37 0.47 0.76 0.55 0.8 0.49 0.99 0.44 0.52 0.51 0.54 0.6 0.55 0.64

std YC 0.51 0.62 0.67 0.46 0.48 0.56 0.45 0.48 0.53 0.47 0.53 0.34 0.5 0.49 0.57 0.48 0.47 0.5 0.49 0.49 0.48 0.58 0.49 0.8 0.5 0.5 0.69 0.42 0.59 0.45 0.58

std ZC 0.51 0.57 0.41 0.49 0.63 0.46 0.51 0.48 0.45 0.49 0.71 0.48 0.58 0.65 0.47 0.5 0.77 0.5 0.5 0.72 0.51 0.53 0.45 0.52 0.46 0.55 0.64 0.59 0.47 0.42 0.55

std X 0.33 0.34 0.31 0.38 0.39 0.77 0.31 0.25 0.39 0.5 0.59 0.53 0.32 0.22 0.4 0.32 0.39 0.45 0.32 0.25 0.31 0.32 0.35 0.27 0.3 0.44 0.34 0.41 0.43 0.3 0.41

std Y 0.52 0.44 0.63 0.38 0.27 0.52 0.32 0.45 0.46 0.46 0.31 0.2 0.46 0.26 0.3 0.29 0.37 0.34 0.35 0.42 0.37 0.61 0.4 0.84 0.35 0.33 0.48 0.28 0.39 0.34 0.47

std Z 0.42 0.4 0.33 0.35 0.56 0.34 0.29 0.41 0.38 0.39 0.56 0.52 0.65 0.44 0.32 0.42 0.77 0.34 0.39 0.58 0.37 0.47 0.26 0.48 0.27 0.46 0.39 0.52 0.39 0.4 0.43

std C 0.26 0.4 0.2 0.3 0.34 0.13 0.38 0.22 0.22 0.22 0.37 0.15 0.09 0.44 0.46 0.35 0.21 0.29 0.28 0.38 0.35 0.18 0.33 0.12 0.37 0.31 0.44 0.26 0.4 0.27 0.31

Appendix I. QRS detection evaluation. Cross-correlation adjustment

ID fp06 fp07 fp09 fp13 fp15b fp16 fp17 fp18b fp21 fp24 fp29 fp30 fp32 fp38 fp38b fp40 fp41 fp42 fp49 fp51 fp53 fp54b fp57 fp57b fp58 fp62 fv01 fv02 fv02b fv03 fv04b fv05 fv05b fv06 fv07 fv08 fv09 fv10 fv11 fv12 fv13 fv14 fv15 fv16 fv16b fv17 fv19 fv21 fv23 fv24

SNR X 32.8 31.3 28.9 30.6 21.7 32.9 38.5 28.4 24.4 26.9 25.2 28.5 30.2 30.7 30.5 15.1 23 32.4 14.2 38.6 31.5 28.2 20.6 23.3 33.4 28.4 34.6 33.2 35.7 35.9 28.7 28.6 24 37 35.2 31.5 33.5 29 25.9 34.6 29.7 25.3 30.1 28.2 27.8 34.3 33.6 26 38.4 23.5

SNR Y 32.5 33.3 28.1 29.2 25.2 20.5 34.3 34.2 14.7 21.2 28.4 25 32 20.2 21 19.1 27.8 29.7 12.1 32.9 26.1 21.1 14.7 14.8 25.7 23.4 33.9 24.7 25.6 34.3 28.1 28.2 24.7 29.9 26.8 30.4 15.3 25 20.6 28.4 31.3 22.7 17.3 20.5 23.6 34.4 33.6 27 35 30.6

SNR Nmin Z 40.6 308 42.1 597 35.3 338 42.2 620 28.3 447 27.8 429 40.3 326 41.9 279 28 302 35.9 342 30.9 328 28.1 368 43.4 400 36.1 316 34.1 245 27 423 30.8 305 34.5 321 24.2 404 45.1 486 35 292 33.4 341 35.7 206 38.7 442 40.7 379 23.9 232 40.7 384 38.8 388 41.4 390 35.6 301 40.9 345 41.6 300 39.7 303 42.2 276 40.4 315 30.6 326 34 357 29.9 320 24.4 279 40.6 322 36.1 425 28.4 431 27 254 29 315 27.1 298 46.9 266 37.4 408 39.6 280 42.4 329 37.5 372

std XY 0.62 1 0.48 1.42 0.83 0.9 0.45 0.6 0.95 0.76 0.49 0.5 0.57 0.59 0.59 0.57 0.6 0.47 1.08 0.47 0.55 1.07 0.86 0.84 0.66 0.58 0.5 0.99 1.05 0.65 1.05 0.49 0.37 0.35 0.47 0.55 0.56 0.58 0.74 0.6 0.89 0.7 0.64 0.73 0.69 0.57 0.39 0.47 0.57 0.52

std XZ 0.54 0.89 0.53 1.06 0.79 0.7 0.7 0.45 0.71 0.82 0.54 0.52 0.51 0.5 0.39 1.06 0.49 0.45 0.79 0.49 0.55 0.63 0.54 0.54 0.52 0.72 0.67 0.4 0.33 0.85 0.83 0.6 0.61 0.52 0.51 0.68 0.43 0.68 0.48 0.51 0.96 0.39 0.5 0.55 0.65 0.91 0.52 0.67 0.63 0.47

std XC 0.47 0.46 0.51 1.11 0.76 0.49 0.59 0.64 0.62 0.68 0.48 0.29 0.5 0.38 0.29 0.6 0.54 0.79 0.64 0.5 0.49 0.51 0.45 0.46 0.39 0.43 0.5 0.57 0.53 0.44 0.69 0.56 0.49 0.45 0.43 0.56 0.49 0.5 0.45 0.44 1.05 0.48 0.56 0.54 0.6 0.48 0.46 0.42 0.48 0.53

311

std YZ 0.51 0.57 0.72 0.86 1.13 0.85 0.76 0.51 0.65 0.53 0.52 0.64 0.62 0.51 0.53 0.97 0.6 0.51 0.85 0.49 0.55 1.36 0.68 0.77 0.51 0.65 0.51 0.86 0.98 0.63 0.69 0.63 0.62 0.52 0.41 0.51 0.55 0.65 0.76 0.53 0.81 0.69 0.79 0.63 0.58 0.85 0.48 0.6 0.72 0.5

std YC 0.5 1.09 0.69 0.85 0.91 0.97 0.63 0.45 0.77 0.44 0.57 0.5 0.58 0.56 0.58 0.54 0.76 0.73 0.89 0.52 0.51 0.98 0.74 0.74 0.54 0.7 0.38 0.77 0.77 0.62 0.77 0.59 0.49 0.48 0.48 0.5 0.53 0.46 0.7 0.48 0.76 0.54 0.64 0.5 0.43 0.5 0.35 0.41 0.56 0.66

std ZC 0.4 0.92 0.23 0.45 0.93 0.75 0.48 0.5 0.51 0.46 0.57 0.5 0.49 0.49 0.36 1.21 0.64 0.92 0.49 0.49 0.57 0.79 0.49 0.48 0.46 0.82 0.46 0.49 0.49 0.81 0.51 0.36 0.38 0.49 0.43 0.5 0.5 0.53 0.51 0.45 0.5 0.54 0.7 0.5 0.5 0.68 0.43 0.54 0.52 0.5

std X 0.44 0.53 0.29 1.09 0.37 0.38 0.38 0.45 0.62 0.68 0.32 0.22 0.35 0.33 0.26 0.39 0.27 0.28 0.67 0.33 0.37 0.17 0.45 0.42 0.4 0.28 0.47 0.47 0.45 0.46 0.73 0.39 0.35 0.27 0.35 0.48 0.33 0.45 0.33 0.39 0.83 0.34 0.26 0.47 0.54 0.47 0.35 0.38 0.36 0.32

std Y 0.43 0.73 0.56 0.86 0.76 0.78 0.46 0.36 0.67 0.35 0.37 0.45 0.48 0.45 0.51 0.18 0.53 0.23 0.83 0.35 0.37 1.05 0.68 0.7 0.47 0.43 0.26 0.81 0.88 0.38 0.7 0.44 0.35 0.3 0.32 0.31 0.44 0.4 0.65 0.43 0.55 0.56 0.55 0.5 0.4 0.43 0.24 0.31 0.48 0.44

std Z 0.3 0.5 0.35 0.17 0.76 0.51 0.53 0.27 0.29 0.43 0.4 0.46 0.38 0.34 0.25 1.01 0.37 0.46 0.36 0.34 0.42 0.75 0.29 0.36 0.32 0.61 0.45 0.25 0.32 0.65 0.34 0.38 0.44 0.41 0.31 0.42 0.33 0.5 0.39 0.34 0.44 0.37 0.52 0.37 0.41 0.73 0.39 0.52 0.5 0.27

std C 0.23 0.63 0.3 0.26 0.57 0.49 0.33 0.39 0.33 0.19 0.41 0.2 0.33 0.3 0.23 0.55 0.52 0.75 0.25 0.36 0.35 0.23 0.28 0.25 0.24 0.49 0.2 0.27 0.11 0.39 0.26 0.31 0.24 0.34 0.31 0.32 0.35 0.21 0.3 0.24 0.5 0.29 0.44 0.25 0.24 0.06 0.25 0.2 0.26 0.44

Appendix I. QRS detection evaluation. Cross-correlation adjustment

SNR X fv25 34.9 fv26 33.7 fv27 40.3 fv28 30.1 fv30 32 fv32b 23.3 fv33 30.8 fv34 28.2 fv35 25.6 fv37 22.1 fv38 27.4 fv39 25.8 fv40 31 fv41 27.3 fv42 36.2 fv43 29.1 fv44 29.2 fv45 37.6 fv48 30.5 fv49 30 fv49b 29 fv50 29 fv51 34.8 fv54 33.3 fv55 30.9 fv56 33.9 fv58 33.4 fv59 35.8 fv61 32.4 fv63 29.6 Ave. 30 ID

SNR Y 26.3 17.1 27.7 32.6 30.7 25.9 28.4 22 17.1 18.1 27.3 27.3 27.2 28.1 27.2 29.1 25.9 25 25.1 31.9 32 30.9 32.7 15.8 31 32.7 21.2 33.3 25.1 24.5 26.2

SNR Nmin Z 37 330 28.8 264 31.2 294 34 293 38 380 35.9 339 35.7 325 30.7 313 24.7 359 30.4 326 31.9 458 34.5 410 37.1 310 34.8 367 36.3 255 33.4 311 24.3 343 40.5 299 33.3 514 32.8 385 25.9 396 38.1 412 37.3 378 36.4 349 33.8 520 37.4 389 38.3 430 37.5 327 38 295 37 383 35 353

std XY 0.51 0.51 0.72 0.47 0.43 0.9 0.53 0.66 0.6 0.55 0.95 0.64 0.49 0.46 0.38 0.49 0.47 0.47 0.43 0.52 0.38 0.72 0.34 1.35 0.59 0.56 0.52 0.46 0.49 0.5 0.63

std XZ 0.56 0.48 0.52 0.48 0.81 0.84 0.45 0.5 0.58 0.61 1.07 0.84 0.7 0.57 0.71 0.49 0.87 0.51 0.55 0.64 0.6 0.49 0.4 0.56 0.5 0.97 0.54 0.74 0.61 0.54 0.62

std XC 0.47 0.5 0.36 0.31 0.49 0.67 0.51 0.44 0.41 0.6 0.9 0.68 0.4 0.35 0.76 0.49 0.43 0.45 0.43 0.49 0.5 0.37 0.39 0.4 0.5 0.5 0.47 0.49 0.49 0.31 0.52

312

std YZ 0.67 0.57 0.74 0.48 0.75 0.47 0.43 0.69 0.54 0.53 0.54 0.57 0.76 0.6 0.64 0.52 0.82 0.46 0.48 0.8 0.66 0.79 0.41 1.49 0.48 0.71 0.51 0.56 0.66 0.52 0.65

std YC 0.43 0.59 0.71 0.43 0.45 0.49 0.38 0.51 0.52 0.49 0.53 0.5 0.49 0.49 0.66 0.49 0.28 0.38 0.37 0.49 0.5 0.59 0.31 1.32 0.51 0.35 0.52 0.4 0.55 0.49 0.58

std ZC 0.51 0.57 0.52 0.5 0.59 0.49 0.46 0.52 0.51 0.47 0.68 0.48 0.66 0.71 0.46 0.5 0.8 0.48 0.51 0.79 0.66 0.54 0.47 0.53 0.46 0.78 0.63 0.58 0.5 0.47 0.56

std X 0.34 0.28 0.3 0.27 0.42 0.73 0.4 0.35 0.39 0.47 0.88 0.63 0.3 0.19 0.48 0.34 0.39 0.36 0.34 0.23 0.25 0.3 0.25 0.23 0.41 0.54 0.33 0.45 0.35 0.3 0.41

std Y 0.41 0.42 0.64 0.34 0.32 0.44 0.3 0.52 0.42 0.34 0.3 0.3 0.42 0.33 0.33 0.36 0.25 0.28 0.25 0.41 0.32 0.62 0.2 1.34 0.4 0.12 0.34 0.21 0.42 0.39 0.46

std Z 0.47 0.39 0.41 0.39 0.65 0.37 0.29 0.43 0.4 0.38 0.55 0.49 0.63 0.55 0.43 0.36 0.78 0.37 0.43 0.66 0.55 0.47 0.35 0.56 0.29 0.75 0.44 0.54 0.47 0.4 0.44

std C 0.23 0.41 0.28 0.25 0.16 0.15 0.31 0.21 0.26 0.34 0.36 0.27 0.25 0.37 0.48 0.34 0.16 0.28 0.27 0.39 0.39 0.17 0.28 0.08 0.32 0.18 0.39 0.26 0.3 0.23 0.31

Appendix J. 2-D VLP detection

features

2-D analysis No. type lead V X c Y Z V X cVLP Y Z V X cVLPj Y Z 1 V X n Y Z V X nVLP Y Z V X nVLPj Y Z V X c Y Z V X cVLP Y Z V X cVLPj Y Z 2 V X n Y Z V X nVLP Y Z V X nVLPj Y Z

from den. QRS RMS 5126 2551 4844 862.3 4658 711.1 4740 1461 8066 158.8 7836 36.84 7958 23.59 7320 381.6 7950 258.8 8212 47.39 7842 23.15 7461 282.5 5208 2097 4790 657 4995 528.1 4697 1234 6818 776 6666 36.05 7895 7.749 7263 302.4 7598 353.4 6834 36.79 7779 8.901 7184 307 4980 2029 4846 1205 4800 543.9 4968 818.5 7620 160.8 7546 63.28 7560 46.14 7440 90.39 7518 169.8 7507 54.39 7608 41.66 7403 92.14 4969 1631 4835 1010 4867 409.8 5085 627.1 7264 148.4 7385 35.39 7701 24.33 7157 55.9 6291 765.4 7282 37.85 7471 27.25 7076 81.17

from level 1 v. mean1 var1 1.829281 56.17229 -0.00441 2.318546 1.00E-02 2.326304 -0.0064 55.05484 2.391814 30.50565 -0.01344 14.71167 3.49E-03 11.08473 0.062089 58.96298 2.247483 40.0474 -0.00213 10.11867 0.003178 7.944362 0.008335 33.95174 1.159471 29.95424 -0.0031 0.384583 -0.00509 0.55629 -0.0043 30.41491 1.227921 28.51809 -0.01092 1.318778 0.009957 1.22971 0.041536 27.98824 1.0724 23.22108 -0.00789 1.007942 0.004457 0.909781 0.00243 29.44396 1.382462 31.5341 -0.00077 1.048648 0.012448 15.72613 -0.00506 16.679 2.695708 40.99898 -3.91E-02 15.11188 0.018763 10.56628 3.78E-02 22.19599 2.282699 33.73634 -0.00262 10.00171 -0.00111 10.92605 -0.00091 19.22474 0.81732 8.604569 -0.00252 0.542842 5.82E-03 4.5039 -0.00323 4.273463 0.983229 7.724779 -0.00931 1.408802 0.012705 1.568906 0.001637 4.034058 0.851795 7.803403 -0.00724 0.903989 0.005486 1.698445 -4.31E-03 4.872162

313

from level 2 v. mean2 var2 10.90394 1017.56 -0.09459 90.43492 -0.15385 141.1532 -0.41972 946.5802 10.14755 508.8749 -0.01397 203.7437 -0.09268 189.9591 -0.15768 805.1571 9.067333 548.6455 0.035569 148.7648 -0.07204 127.2202 1.64E-01 443.4176 8.674468 652.9912 -0.12117 46.58293 -0.08973 76.05465 -0.32716 616.5823 7.547418 542.1271 -0.05454 46.99881 -0.01442 36.58795 -0.19295 420.6105 5.654233 364.4885 -0.00376 35.96279 -0.02886 22.95002 -2.15E-01 413.0241 8.401324 456.3989 -0.0926 117.8684 0.222396 127.7329 -0.18605 295.2704 10.5775 561.768 -0.01914 208.6849 0.100911 186.4571 0.028175 337.0607 9.043506 468.7129 0.036663 155.3982 -0.07704 144.6714 -0.1066 270.3417 5.803643 220.1876 -0.06763 74.22043 0.161189 61.84841 -9.85E-02 124.2575 5.359396 171.1534 -0.09582 49.18418 0.084578 40.02326 0.052066 112.2146 5.274958 198.4696 -0.00373 35.51132 0.005631 38.14075 0.04496 111.3088

from level 3 v. mean3 var3 60.47673 21032.17 -2.478122 5901.074 -1.866214 6391.827 -3.1603 12930.8 18.11365 1933.01 -0.571124 543.4708 0.365742 428.2513 -2.527684 4281.027 16.72254 2010.381 -0.399545 454.7744 0.027448 325.9996 0.806044 1979.262 52.8537 16139.59 -0.374851 3823.222 -0.755626 4331.498 -2.650668 10352.55 26.34085 5844.555 -0.756981 214.3753 -0.349309 152.8839 -2.140527 3193.079 15.45252 2327.071 -0.093754 221.6011 -0.172974 123.4533 -1.33618 2585.316 41.61626 10063.02 -1.744606 6289.187 -0.989977 2567.369 -0.695169 3499.878 17.18629 1613.165 0.881573 607.8599 0.838682 512.6778 -2.540713 1095.106 17.31899 2078.745 0.023524 628.2099 0.40353 452.9868 -1.137359 1382.317 33.4738 6920.195 -1.448549 4699.89 -0.762383 1696.832 -0.466532 2109.095 13.28623 1308.278 -0.69236 414.726 0.859325 196.6596 -0.007567 928.6916 21.87911 3896.08 -0.122338 377.958 0.202542 245.7858 0.380304 1256.541


features


from den. QRS RMS 5880 2253 5340 1897 4260 743.6 4860 398.4 8460 111.9 7920 81.96 7860 24.35 7380 23.85 8349 111.4 7786 92.49 8266 19.22 8527 20.31 6093 1704 5726 1126 4751 583.7 3947 276.4 8449 63.16 7513 66.3 7827 7.024 7157 6.818 8411 58.08 6829 126 8268 4.663 7049 6.04 4882 3699 4680 1910 7920 488.7 4898 1937 7882 61.06 7980 25.18 10860 23.13 7778 28.66 7781 60.53 8158 21.73 10694 21.26 7857 25.67 4976 3191 2990 1787 4007 422.2 4944 1713 7940 17.7 7221 6.921 7238 5.887 7536 19.22 7753 21.49 7044 11.69 7111 5.508 7622 26.73

from level 1 v. mean1 var1 1.035085 21.66771 0.003373 22.38229 0.000327 0.53841 0.011227 0.292619 2.458605 31.81425 0.011962 16.5864 1.62E-02 10.61901 0.014467 10.19888 2.087756 26.44407 -0.00759 16.31901 9.02E-03 7.19E+00 3.37E-03 7.27E+00 0.698926 8.303848 -7.64E-03 8.37137 0.002404 0.535311 0.003756 0.338759 0.882939 5.037774 -0.00639 2.956323 0.006652 1.29901 -0.00021 1.38608 0.717293 4.040507 -0.00324 2.611439 0.005258 0.858322 -0.00013 0.941016 0.663134 9.750188 0.009852 9.522179 0.001702 0.127968 8.74E-03 0.550644 2.382905 30.54394 -0.01164 14.73843 0.003295 11.13068 1.72E-02 10.31863 1.996331 22.25194 0.006838 8.984098 0.003235 8.007771 3.61E-03 7.94E+00 0.516201 3.676898 -0.00192 3.043293 0.0011 0.148278 0.005855 0.707098 0.782426 3.840384 -0.00854 1.455872 6.20E-03 1.277559 -2.08E-03 1.455217 0.597171 2.505979 -0.00653 0.877187 0.003221 0.894429 2.34E-03 1.026866

314

from level 2 v. mean2 var2 8.037132 656.5877 -0.01133 630.6048 0.064811 118.9928 0.131902 87.88532 10.56404 576.6212 -0.26077 303.5094 -0.04576 188.6398 -0.01175 192.6495 8.48577 398.0371 -0.0507 230.0974 -0.03323 116.5564 0.009662 125.3674 6.077936 419.873 -0.0291 404.2615 0.063928 64.32534 0.042565 45.86214 5.08634 152.2474 0.080149 110.7285 -0.01847 34.48782 0.008688 33.91453 3.951087 107.8403 0.038405 89.02427 -2.11E-02 21.98599 0.008686 20.54887 6.920133 402.2475 0.156118 246.8105 -0.08095 35.4376 0.193326 170.3815 9.880068 496.4077 0.011932 204.5782 -0.10945 192.0005 0.024165 197.4031 8.046668 344.9116 -0.00259 145.2306 -0.06681 126.5676 0.015406 136.9243 5.548352 268.403 0.040691 146.2565 0.007999 21.77515 0.16046 132.0543 4.148431 95.87864 0.03206 45.91572 -0.01813 34.57541 -0.03478 30.95173 3.273627 65.92968 0.007413 29.80123 -0.01525 22.74431 0.034259 24.60931

from level 3 v. mean3 var3 51.92112 20275.13 -4.216813 16233.22 2.907112 7110.268 -0.367666 5231.613 18.62887 2047.272 -2.060785 1460.624 -0.268123 529.9686 0.074372 424.5749 16.53075 1717.28 -0.770654 1406.435 0.211065 327.5163 -0.145799 298.9899 41.42496 14156.01 4.140459 9017.402 2.440598 5223.115 -0.381959 2927.413 11.93761 996.2264 -1.127615 945.4468 -0.021382 184.6908 0.031487 116.0183 10.02042 832.608 -0.066901 1175.876 0.155357 105.7384 1.58E-01 84.85998 54.0556 21716.18 0.035791 6536.077 -0.500036 3276.955 1.374273 15315.53 15.60326 1171.512 0.048673 505.6628 0.211855 413.4831 0.373565 481.0624 13.22875 872.7937 0.013433 381.3081 0.08559 330.5686 -0.08953 321.461 47.12384 17000.48 0.451771 4969.469 0.163986 2170.573 1.024802 12467.07 8.567073 369.7104 0.134011 179.2307 -0.204001 129.0737 -0.098422 145.6555 7.339888 277.2281 -0.085297 123.8628 -0.010349 115.9052 0.305376 129.7607


features


from den. QRS RMS 5220 2426 4380 628.9 4920 557.2 4620 1619 7740 181.1 7200 78.01 7918 28.29 7320 196.5 7634 225.6 7609 57.75 8751 13.83 7459 170.2 5265 1994 4945 485.5 4465 405.1 5191 1412 7684 147.6 7109 49.16 7125 18.64 7187 157.2 7408 205.6 6954 47.45 7030 23.58 7130 165.2 4420 2499 3840 269.2 7980 822.3 4426 1798 7500 103.8 7080 24.67 10800 24.82 7380 126.1 10181 174 10570 20.46 10690 22.95 7449 129.8 4465 2076 2840 174.6 3198 667.4 4458 1576 6741 446.2 5811 4.884 6470 6.758 6909 306.7 7379 146.6 6350 3.21 6358 12.33 7081 268.4

from level 1 v. mean1 var1 1.428043 18.94599 4.88E-03 6.994086 1.32E-02 5.053913 0.008368 11.38245 2.558272 38.02111 -0.01276 13.94628 0.00909 11.07404 0.000252 18.19592 2.199164 30.20793 -0.0049 10.03479 -0.01182 5.771487 0.00733 16.54858 0.806122 5.34487 0.008381 1.345269 0.001759 1.9036 0.003397 2.979997 0.857468 5.051092 -0.00627 1.333119 0.002578 1.226871 -0.00229 3.044729 0.718023 4.322191 -0.00405 0.946704 0.002591 0.798206 -0.0017 3.035191 0.845945 7.105649 2.83E-03 0.240444 0.002144 5.181281 3.21E-02 2.148413 2.372034 30.2005 -1.31E-02 14.72264 0.003353 11.12077 0.021154 9.955726 1.960735 2.14E+01 -0.00634 9.396062 0.003763 7.87E+00 0.005268 7.69E+00 0.629243 3.096133 0.005743 0.196397 -0.00113 1.189335 0.025155 2.100483 0.667019 3.036216 -7.52E-03 1.144856 0.007415 1.368656 0.015773 1.378122 0.634155 2.729058 -0.0038 0.660073 0.006464 1.02611 -3.71E-05 1.378429

315

from level 2 v. mean2 var2 11.63626 985.5863 0.211678 195.4869 0.16472 554.3384 -0.20721 415.6812 10.03485 493.1693 -0.02197 197.6727 -0.02623 186.8869 -0.04447 200.9119 8.592661 396.7619 0.022057 145.5637 0.053535 70.77128 0.006727 185.1828 8.625495 594.7742 0.06991 77.73179 0.055362 349.443 -0.13222 250.3283 4.430986 106.6067 -0.04091 43.1044 -0.00758 35.37655 -0.04939 48.07835 4.109902 105.6209 0.015415 40.0847 -0.01784 27.01042 0.064978 55.89693 10.17884 711.0122 0.024475 60.50639 0.112808 241.2725 0.236762 503.9021 9.769701 488.3214 0.01136 203.5813 -0.09198 192.6672 0.095483 188.6732 7.936516 334.3635 0.014909 134.0816 -0.05585 125.7462 0.049792 135.2199 8.2453 482.9172 0.049212 26.22195 0.00939 165.4889 0.226734 356.4198 4.381527 119.872 0.024861 37.66838 -0.04904 38.26573 -0.25115 43.62495 3.393943 66.91133 0.020855 21.66746 -0.00058 24.91715 -0.00907 36.14045

from level 3 v. mean3 var3 60.69771 25662.87 0.303793 4454.067 0.14558 13908.73 -0.090144 11489.53 16.74322 1437.755 -1.156998 625.7966 1.14319 559.5442 0.365051 662.1376 15.8163 1438.428 -0.423053 579.9874 0.081766 238.3529 -0.165449 697.0296 49.65133 18114.85 -0.075671 2917.484 -0.339351 9139.631 -0.116921 8793.326 10.61084 634.0338 -0.950529 258.7706 0.495353 270.2785 0.201287 278.4699 11.75505 932.3321 -0.071428 356.2196 -0.002797 254.7159 0.422738 413 65.41285 24359.21 -0.578774 2689.07 -2.384353 11763.83 -0.609757 13714.41 15.71507 1195.595 0.098223 509.5216 0.295303 454.022 1.218848 535.7736 13.49222 935.6197 -0.014847 355.5551 0.173896 344.7018 0.544936 392.8718 54.56664 17270.84 0.40511 1373.589 -0.763548 8707.263 -0.089743 10142 15.87208 2371.161 0.073646 133.3909 -0.391549 173.9472 -2.007026 1103.312 8.606401 496.9802 0.110974 85.27638 0.267822 173.9609 0.132117 590.6691


features


from den. QRS RMS 6000 1970 5494 1841 6000 109.1 6060 1194 8760 61.44 8820 24.62 8700 25.39 8880 23.03 8643 58.29 8687 22.58 8753 21.73 8705 22.7 5968 1726 5004 1490 6090 59.96 5620 1278 8735 19.31 8112 6.973 8316 5.866 8490 9.713 8470 27.08 8058 5.064 8155 5.631 8304 38.06 4784 2411 4184 1736 5188 270.6 4140 779.7 7140 145.5 7140 34.92 7724 49.72 6840 85.35 7496 152.7 7005 40.46 7648 43.79 6796 92.51 4312 1986 4315 1496 3357 178.9 4205 618 7073 94.6 7161 19.64 7106 33.5 6603 87.77 7214 100.1 6914 26.07 6247 26.02 6504 87.98

from level 1 v. mean1 var1 0.511907 3.340759 -0.02416 2.785265 1.26E-03 0.906955 -3.45E-03 0.442821 2.377448 30.40069 -0.01302 14.70493 4.57E-02 11.09873 0.005192 10.44339 1.955677 21.44518 -0.00612 10.09201 0.00579 7.312167 0.002918 7.798715 0.44147 2.489845 -0.0153 2.516614 0.000601 0.152101 -0.00716 0.863286 0.737261 3.433593 -0.0095 1.403945 9.22E-03 0.914133 0.00382 1.489352 0.566493 2.268188 -0.00472 0.998732 0.003289 0.56118 0.000371 0.995945 0.652532 5.980033 -6.18E-04 0.647119 -1.93E-03 1.307627 0.006581 4.471783 2.544417 33.84806 -9.28E-03 14.71786 0.00531 11.39597 0.022913 13.96051 2.081811 24.9202 -7.02E-03 1.01E+01 0.004791 7.696003 0.004325 11.81817 0.451011 1.586179 0.000387 0.781047 -0.00761 0.241134 0.00245 0.771405 0.80119 3.893249 -8.25E-04 1.829076 6.55E-05 1.151631 -1.45E-03 1.602112 0.64553 2.82927 -0.00336 1.003177 -3.71E-05 0.804708 -0.00209 1.448794

316

from level 2 v. mean2 var2 6.407677 466.8192 -5.79E-01 713.8912 0.056334 42.94972 -0.51986 90.6327 9.872648 493.6172 0.0151 202.9919 0.060851 190.5144 0.015831 199.6247 7.931186 336.382 0.020907 144.1923 -0.05651 119.2862 -0.00069 135.6888 5.239708 395.1342 -0.39707 547.7592 0.028517 12.5101 -0.22227 180.8406 4.12935 95.32321 0.019269 49.59216 0.03403 26.03574 0.005662 35.77406 3.089507 58.78237 0.008009 29.83471 -0.00658 16.77523 2.17E-02 22.37476 7.567296 346.1318 0.028746 189.7103 -0.0947 74.46881 0.087106 142.3291 9.922959 500.0236 0.073963 204.0591 0.185521 180.6563 -0.05842 210.8035 8.219126 360.5442 0.024317 143.2882 0.007504 129.8923 0.000617 152.078 5.770838 218.6142 0.033757 148.4703 -0.08008 19.25234 0.062667 84.27264 4.545741 114.8546 0.040982 59.71355 -0.1265 37.95548 0.017127 41.24279 3.651711 78.40569 0.023289 31.41121 -0.04746 27.43515 0.045047 40.74526

from level 3 v. mean3 var3 33.19142 9817.666 1.311681 29124.95 1.433333 1082.294 -4.981717 4279.762 14.95284 1093.934 0.125332 507.7794 -0.290467 398.7769 -0.039965 410.7173 13.30625 894.1001 -0.008532 383.3071 0.182453 337.6986 -0.257731 335.5894 30.3749 10157.78 2.254459 22844.56 0.684371 482.8842 -4.027449 11172.95 8.700675 393.866 0.195626 216.0661 -0.012899 105.0483 -0.146025 148.9131 6.792865 256.3117 -0.002223 103.271 0.078038 109.7812 0.34074 118.3834 59.01023 21832.55 0.631671 16653.25 -0.271034 1353.603 0.141491 7362.917 17.62228 1697.836 0.576303 525.8976 1.764437 954.904 0.514585 549.7218 15.11395 1240.995 0.285878 438.1094 0.75042 589.651 0.461242 411.7761 50.35515 16862.87 -0.206354 13492.2 -1.190106 702.8314 -0.227259 5164.375 11.10804 743.3545 0.559252 218.2421 0.728028 473.6768 0.022672 229.1786 9.22129 521.8666 0.182021 175.5968 0.356786 285.0096 0.135927 246.4972


features


from den. QRS RMS 5630 2398 5700 1357 5280 289.9 5700 1023 8450 97 8460 25.52 8160 23.59 8640 35.83 8396 97.73 8374 22.75 8526 23.15 8479 57.58 5299 2053 3313 1851 4388 471.4 5317 878.8 5434 1450 8576 7.266 7624 8.391 7849 58.7 8199 109 6927 86.68 7513 8.808 7086 63.56 4998 2718 5122 1445 5100 737.9 4620 1256 8100 60.2 8220 24.72 8100 23.28 8220 23.63 8002 55.83 8377 21.71 7981 21.31 8070 22.08 5436 2059 3347 1232 4774 565.5 4606 1043 7997 16.39 7424 5.771 7514 6.158 6902 9.213 7330 95.35 7268 4.882 6796 5.904 7748 11.91

from level 1 v. mean1 var1 1.446317 36.56968 -3.86E-05 0.195291 1.33E-02 33.04414 -1.52E-02 5.420992 2.381635 30.46975 -0.01298 14.665 0.003502 10.99512 0.016101 10.59906 2.023747 23.20376 -0.00399 9.895382 8.03E-03 8.243414 1.95E-03 8.756023 0.837394 12.49644 0.005876 0.351209 -0.01731 11.80827 -0.01361 1.076067 0.895079 11.77575 -0.00228 1.608934 0.006286 1.37101 0.004946 1.901443 0.69862 4.016361 -0.00594 0.783007 0.013113 1.534549 -4.92E-05 1.407914 1.159037 10.23617 0.038164 8.09082 -0.00384 2.336368 -1.13E-02 1.179029 2.377129 30.40416 -0.01443 14.71717 0.003047 11.04343 0.005573 10.42054 1.994136 22.21031 0.002621 9.093708 0.003686 7.955182 0.002526 7.856162 0.688444 4.341519 1.17E-02 2.633577 4.74E-03 1.496326 -0.00862 1.188816 0.788843 3.89766 -7.59E-03 1.429296 5.02E-03 1.187468 1.73E-03 1.731322 0.561536 2.391041 -0.00602 0.88015 3.78E-03 0.735474 3.35E-03 1.229969

317

from level 2 v. mean2 var2 8.44663 464.2493 -0.05011 64.17827 4.21E-01 292.8027 -0.3159 177.6338 9.848902 490.4943 0.00091 202.4242 -0.10364 187.383 0.164325 197.5769 8.155878 347.6752 0.014865 144.8381 -0.05963 124.0702 0.018809 140.6879 6.642167 279.8182 0.116529 54.24423 -0.34639 168.8459 -0.29012 120.559 5.890841 221.9154 0.016497 49.36558 0.005151 35.1289 -0.02679 60.59978 3.852301 89.69752 -0.08847 30.5091 -0.02789 23.90993 -0.03743 45.5802 11.12116 940.5391 -0.13198 376.2932 0.220008 393.9016 -0.22193 296.4673 9.822085 492.5612 0.003085 202.734 -0.10567 190.7718 0.006133 197.085 8.006088 341.9374 0.004027 142.5649 -0.06016 124.9013 0.003709 135.0509 7.704177 540.6565 0.095252 239.3888 0.157183 250.3782 -0.19884 192.7713 4.32661 104.8105 0.02834 43.7161 -0.01126 32.27479 0.026185 45.7859 3.310611 73.03031 0.028173 30.20028 -0.01973 19.58175 0.029873 29.18366

from level 3 v. mean3 var3 60.36947 25552.59 -1.751179 7902.279 -0.211594 6522.683 -2.398853 14763.69 16.20134 1335.345 -0.162774 507.4993 0.199732 401.511 0.967693 580.4089 14.72702 1202.716 -0.03193 388.3195 0.001316 325.3016 0.061351 646.1789 52.54508 20091.3 1.095643 6772.64 -0.499214 9013.941 -1.928812 11936.34 37.02667 11918.89 0.01472 183.3408 -0.277015 142.3785 -1.68E+00 826.7474 10.42926 879.0385 -1.068162 477.9409 -0.179948 92.94476 -0.792201 749.9891 60.98253 26511.13 -1.327713 11880.63 -2.706062 10133.11 0.352761 8646.747 15.23452 1129.85 -0.024089 508.6205 0.242193 422.5316 -0.210359 407.2562 13.22916 874.3352 -0.013115 379.9768 0.067147 326.1197 -0.314348 332.7122 45.77905 17742.97 0.349598 9215.97 -3.673923 7010.384 0.275334 6041.424 8.532449 368.4236 0.15803 150.03 -0.255419 137.8827 0.150735 160.8495 9.060956 796.9319 0.174827 129.9149 -0.070324 111.1398 0.143768 142.3671


features


from den. QRS RMS 5640 1030 5820 460.6 5030 481.8 4368 273.5 8760 70.51 8820 26.27 7920 29.71 7740 24.27 8657 117.7 8703 25.99 8086 75.03 8474 23.56 4994 716.6 5762 328.1 3641 344.8 4623 181.2 7904 42.49 7652 9.661 6202 35.63 7486 16.43 8125 136.2 7550 8.362 6541 76.09 7464 28.45 5160 3923 4740 2030 4920 356.8 5160 2044 8040 74.67 7560 26.1 7860 24.72 7920 52.35 7934 77.97 7426 23.18 7738 22.34 8004 40.22 5242 3420 3939 2626 4985 231 5208 1826 7993 37.26 7465 8.838 7295 7.542 7789 41.17 7977 34.5 7235 7.718 7621 7.521 7569 50.47

from level 1 v. mean1 var1 1.721522 19.01584 -0.00846 5.659979 -0.00243 9.980984 -0.00013 6.548498 2.379479 30.51697 -0.01078 14.73924 7.57E-03 11.08835 0.015549 10.32033 1.977323 21.64902 -2.70E-03 9.77E+00 0.008412 8.219892 6.03E-03 7.506611 0.492698 1.925338 -0.00776 0.599931 6.76E-03 1.234933 5.10E-04 0.302738 0.785296 3.800811 -1.03E-02 1.290913 -0.00411 1.375467 7.96E-04 1.542605 0.579546 2.356101 -7.54E-03 0.759027 0.003785 1.006882 0.000141 0.915702 0.61673 3.596873 3.04E-02 2.468387 7.06E-03 1.106518 -1.38E-02 0.353802 2.372801 30.23996 -1.25E-02 14.67169 0.005385 11.03617 1.30E-02 10.12922 1.963088 21.60281 -0.00693 10.0012 4.63E-03 7.57E+00 0.00462 7.767743 0.591488 2.990103 0.004488 3.878428 -0.00347 0.798015 -7.21E-03 0.370114 0.783571 3.989398 -0.00429 1.832892 0.006156 1.220796 0.00051 1.518349 0.623742 2.608296 -0.00625 1.008685 0.00511 0.887066 -0.00178 0.907687

318

from level 2 v. mean2 var2 7.240417 283.8842 -0.26143 128.3921 0.17761 127.6771 0.011158 73.00973 9.809712 492.7505 0.044914 203.2237 -2.99E-02 188.6883 -0.01737 197.4791 7.930512 331.7373 0.031547 141.9389 -0.0697 122.6664 -0.00989 129.1148 4.393353 112.2046 -0.09202 53.17629 0.118298 47.49234 -0.01085 29.28733 4.182527 97.51882 0.064277 36.70293 -0.13604 37.95572 0.039677 39.75662 3.167988 59.4857 0.021283 25.52019 -0.04967 23.20876 0.018923 21.49391 9.483058 705.8333 0.667376 502.9748 -0.3729 206.7964 -0.02868 84.88996 9.788376 489.5317 -0.01225 201.8094 -0.05492 186.9135 -0.00908 197.3237 7.901654 332.9706 0.007529 140.4556 -0.04688 119.5713 0.027894 134.0681 7.514454 463.7193 0.794354 743.0932 -0.28693 116.0059 0.01659 53.95782 4.326714 104.5551 -0.00245 51.98143 0.007072 29.3978 -0.00866 41.76919 3.371966 67.16661 0.018593 30.44168 -0.0189 21.56055 -0.01667 24.46802

from level 3 v. mean3 var3 39.17781 7735.229 -2.359173 3448.758 0.184375 3005.885 -1.177724 2795.63 15.76664 1210.998 0.322576 516.5216 0.625812 467.605 -0.201924 423.1001 13.63891 953.388 0.156105 404.4171 -0.388725 419.349 0.019588 335.7021 29.76393 4546.67 -1.476248 1957.209 0.117349 1895.754 -0.53642 1617.188 8.809436 437.439 0.485035 122.3043 -0.862589 292.9139 0.62692 160.8314 8.732164 565.6428 0.148146 108.3129 -0.615793 242.4925 0.489058 196.9523 57.18371 23403.89 2.601248 12820.55 -4.655339 7006.432 2.895759 5524.511 16.21677 1298.071 -0.279948 514.329 0.5707 461.8267 0.834379 587.4086 13.54515 930.8058 -0.191284 379.3944 0.37557 332.1154 0.092475 371.2662 48.61871 17863.81 2.859196 28879.59 -3.495133 4439.613 2.884509 4250.739 9.578633 472.7784 -0.157611 213.3305 0.289354 139.7658 0.012431 263.1575 7.949196 336.2984 0.029468 130.3274 0.177953 131.2907 -0.226615 218.8217


features


from den. QRS RMS 6060 952.2 5804 474.2 5022 154 5700 494.3 8950 71.36 8520 27.35 9060 22.82 8760 25.38 8946 78.43 8401 25.52 8946 17.55 9011 42.64 5485 689.5 3553 378.5 3851 73.24 5728 368.1 7355 284.1 6479 8.258 8076 4.122 8371 40.91 6214 453.9 6763 8.589 4129 51.42 7490 40.25 5388 1101 4824 695 3720 249 5520 520.6 8268 59.61 8280 24.59 7320 22.34 8220 24.03 8230 52.8 10983 21.94 7286 18.85 8302 21.32 5142 880.4 4517 558.3 4165 145.7 3925 487.4 7798 90.14 7533 5.413 7358 4.714 5393 217.8 7947 24.78 7504 5.272 7248 3.632 7941 10.31

from level 1 v. mean1 var1 0.566034 2.81162 -7.83E-03 0.187207 0.012818 0.185185 -0.00109 2.845319 2.372809 30.32353 -0.01576 14.76486 0.003936 10.95706 0.006537 10.36212 1.922707 20.51343 -0.00503 9.649384 0.004097 6.894214 -0.00112 7.427324 0.25353 0.507113 -4.60E-03 0.109883 0.004401 0.16134 -1.14E-03 0.395257 0.551665 2.316409 -0.00176 1.413341 4.25E-03 0.620136 -0.00333 1.563529 0.373777 1.196443 -0.00383 0.855744 -0.00039 0.265307 0.001221 1.019042 0.282419 0.760249 -9.97E-05 0.282373 2.27E-03 0.348716 0.00388 0.329193 2.381765 30.45144 -0.01353 14.72924 1.65E-02 10.7169 0.013949 10.22531 1.944886 21.25951 -0.0066 9.77E+00 8.53E-03 7.36E+00 0.003567 7.71827 0.336782 0.800595 0.000188 0.289941 0.001749 0.264536 0.005285 0.555614 0.645247 2.934402 -7.05E-03 1.10676 0.006442 1.067944 0.016707 0.930845 0.538183 2.084959 -0.00495 0.941795 4.89E-03 0.637787 4.45E-06 1.058101

319

from level 2 v. mean2 var2 4.116776 108.1487 -0.07726 11.17701 0.13172 41.93541 0.047255 90.7713 9.818761 489.4435 -0.02567 204.0335 -0.09437 187.4429 0.028366 195.1084 7.839438 324.9615 0.027447 140.8875 -0.05405 110.8188 0.024973 131.9442 2.631996 46.99522 -0.03513 5.578021 0.077641 16.53901 0.033016 40.27609 3.52662 73.98731 0.111358 48.61401 -0.00335 18.68834 -0.06194 43.24782 3.035143 58.66173 0.042315 28.26456 -0.04106 14.0448 0.030081 35.65467 5.154499 198.4153 -0.02799 67.75826 0.046539 88.32089 0.144295 98.96811 9.846281 493.9695 0.004471 202.4856 -0.02949 187.7193 -0.03696 197.6004 7.875877 330.3584 0.022365 140.628 -0.04735 116.3444 0.013601 133.5407 4.135714 114.1773 -0.0494 34.90757 0.069424 32.91635 -0.06302 87.34635 3.682333 84.76742 0.019742 36.90135 0.00726 29.88237 0.019899 49.49509 2.991345 56.85434 0.021023 31.33627 -0.01125 16.41885 0.015145 23.53502

from level 3 v. mean3 var3 30.13381 5224.13 -0.045577 497.8772 -1.166817 2082.765 1.648269 3917.988 16.22773 1292.639 -0.413183 528.5733 0.307193 418.5572 0.075816 489.3863 13.74702 985.6391 0.114906 416.4425 0.137419 287.9445 0.28166 378.4734 22.47342 3013.723 -0.776483 289.3652 0.137967 967.259 1.170757 2472.631 14.30504 1478.415 0.430772 213.1984 0.040863 74.06563 0.350256 412.0464 18.1154 2184.163 0.478755 152.9461 -0.420688 662.6579 -0.050146 456.9704 38.07047 10885.79 -1.443141 2086.726 0.435451 3056.736 -1.521255 8259.205 15.36393 1144.338 -0.002323 505.0887 -0.31345 447.7363 0.09296 444.0439 12.97507 844.6733 0.037483 372.5623 0.070953 309.39 -0.114535 328.8821 32.47211 7269.972 -0.447887 1231.981 0.065357 1349.189 -2.288242 6853.803 8.903782 713.2931 0.141437 131.4689 -0.004612 110.9335 0.540774 3094.206 7.044443 278.3725 0.073967 118.2402 0.039348 84.9606 0.122777 114.4885


features


from den. QRS RMS 8220 2143 3960 1176 5280 607.7 7420 1050 8040 65.93 7620 24.66 8100 30.04 11100 23.3 10878 58.96 7982 21.7 8005 24.91 10943 21.72 5509 1704 3019 954.8 4674 474.4 4106 862.4 7651 41.21 7090 5.511 7488 10.3 7538 12.99 7886 24.18 5673 4.44 7363 9.269 6673 36.38 4320 5001 4440 1468 3780 1919 4320 2363 7860 59.81 7860 24.7 7980 23.21 7980 23.22 11228 52.87 11123 21.71 7824 20.74 7827 21.9 4338 4309 3943 1475 2857 1644 4341 2047 7678 41.47 7963 6.974 6811 6.144 7692 7.183 7665 15.28 6872 4.42 6776 5.178 7452 15.51

from level 1 v. mean1 var1 0.492307 5.888186 -0.00052 0.52115 -0.00855 5.557134 -0.01215 0.170796 2.393126 30.44624 -0.01346 14.71119 0.004043 11.0925 0.005089 10.44861 1.991109 22.0943 -0.00652 1.01E+01 0.003371 7.834636 0.002729 7.810734 0.352983 1.459734 0.001374 0.675636 -0.00162 0.846995 -0.00558 0.167979 0.72317 3.495144 -0.00982 1.552086 0.003315 1.305227 -0.00014 1.292272 0.604917 2.507622 -0.0051 1.016099 0.003407 0.807018 -3.15E-04 0.971809 0.933522 8.79035 0.000502 1.900538 0.001508 4.564027 1.74E-02 3.207889 2.382323 30.52013 -1.37E-02 14.74026 0.008532 11.11816 0.006116 10.46919 1.865075 20.33339 -0.00343 9.36E+00 0.004348 7.914506 0.002476 8.072497 0.918324 7.650324 0.003388 1.648796 0.003825 4.099418 7.84E-03 2.796798 0.758252 3.830208 -0.00352 1.552752 0.006302 1.458044 0.0009 1.52443 0.626167 2.690336 -0.00566 1.019404 0.002909 0.895025 -0.00247 1.112514

320

from level 2 v. mean2 var2 4.535552 184.8738 -0.02719 145.0018 -0.177 50.14734 -0.25117 40.83418 9.758484 490.9007 0.004311 203.3261 -0.03454 186.3237 -0.00028 198.2309 7.985694 339.2136 0.018503 143.5012 -0.05617 123.1114 0.003985 134.9218 3.423336 117.7296 0.023574 106.115 -0.00499 20.77156 -0.10836 16.70239 3.951108 92.81909 0.028822 46.0561 -0.07305 35.03363 0.009468 33.00194 3.327969 65.11182 0.011033 30.33881 -0.01752 20.26789 0.029188 25.16198 15.379 2008.317 -0.11737 413.9762 -0.0506 1111.088 0.179321 721.2705 9.855077 495.0061 0.000111 203.6562 -0.08627 191.5209 1.53E-02 198.5468 7.624151 328.5448 0.011385 143.9817 -5.50E-02 128.2 0.008575 138.4774 12.83895 1527.57 0.063065 275.1743 -0.00194 905.3835 0.079066 515.6935 4.306723 120.1698 -0.0069 48.41708 -0.00306 35.75159 -0.00586 42.36283 3.368801 67.3976 0.022169 29.01372 -0.00859 23.45092 0.000117 25.50342

from level 3 v. mean3 var3 36.1819 10180.65 0.399569 8808.228 -1.917393 1857.675 -1.089706 1578.699 15.88189 1234.169 0.021357 509.2917 0.868487 509.3064 -0.357002 430.985 13.15711 878.8375 0.011253 377.1911 0.234635 346.8941 -0.274432 319.5763 29.13762 7285.424 0.619983 6381.513 -0.841295 1327.495 -0.605558 989.2329 9.219053 436.1086 0.165755 137.5418 -0.084373 224.43 0.289967 154.2317 7.74867 323.5079 0.061874 115.0669 -0.110037 150.1688 0.6072 129.99 89.41404 67350.84 -1.835658 7839.666 0.671034 47314.47 1.342993 20191.64 15.28155 1134.924 -0.04123 508.8951 0.453279 419.2274 -0.183496 419.4375 12.57218 843.1664 -0.002073 382.9555 0.126077 335.2721 -0.25971 326.5672 79.19538 54838.7 0.755313 5885.63 0.681727 39447 1.533854 15942.62 9.732145 851.5508 -0.029204 202.6543 -0.10139 166.5955 -0.083198 160.9074 7.572928 289.9331 0.094505 105.7212 0.010612 129.0106 0.146838 109.979


features


from den. QRS RMS 8114 2364 8460 907.7 8640 521.7 4740 681.3 11280 68.08 11280 30.26 7980 25.09 7980 23.28 11177 84.84 11242 27.22 11107 25.79 7820 38.36 5526 1465 4719 733.6 4584 892.6 4838 580.8 7938 38.62 8108 9.648 7494 8.801 7828 23.01 7874 56.98 7222 11.3 7358 11.64 7472 64.7 4842 10603 4500 2788 4740 1454 5100 7286 7798 61.85 7860 24.71 7980 23.08 7860 30.27 7694 65.78 7728 22.72 7895 20.41 7464 32.87 4515 12346 3185 2464 4857 1250 4227 10960 5281 8034 5457 27.83 7825 6.234 7412 39.02 5754 5702 7552 6.7 7721 5.442 7152 121.3

from level 1 v. mean1 var1 2.093321 37.37675 -0.01698 7.039623 -0.04352 24.42593 1.76E-02 6.588308 2.388136 30.13118 -0.01931 14.46067 0.003552 11.07022 0.003966 10.40137 1.980598 21.8072 -0.00285 9.727904 0.004812 7.74925 4.40E-03 7.89E+00 0.844047 9.400832 -0.00479 1.891058 -0.00321 8.388638 1.65E-02 1.128753 0.734398 3.512132 -4.04E-03 1.439707 6.41E-03 1.28888 3.12E-03 1.413339 0.614969 2.588036 -0.00586 1.033745 3.74E-03 0.808296 -1.11E-03 1.204947 1.131517 32.84458 -0.00311 0.284334 -0.00238 0.445787 1.50E-02 33.374 2.382979 30.53825 -0.01377 14.73278 0.003936 11.10013 1.09E-02 10.35101 1.981414 22.03014 -0.00603 10.26239 0.003225 7.803994 5.83E-03 7.62E+00 0.97181 15.72342 0.017296 0.439587 0.003533 0.525406 -0.00988 15.62585 0.860493 12.53753 0.017293 0.787099 6.39E-03 1.552807 0.002596 1.78434 0.766592 10.45724 -5.33E-03 1.027336 0.003784 0.752218 0.002823 0.868383

321

from level 2 v. mean2 var2 9.795973 740.4584 -0.41789 220.5216 0.674293 277.4434 0.344766 181.7356 9.938744 496.1231 0.04064 206.7658 -0.09021 189.7821 -0.01529 197.8802 8.104633 348.4275 0.056945 148.1721 -0.05005 126.7636 0.032412 137.9485 5.869926 321.8104 -0.37439 124.3857 -0.12761 231.2491 0.173755 99.18134 4.141163 97.12051 0.027788 45.34185 0.036832 30.75242 0.04943 40.30585 3.383478 67.45633 0.013107 30.27214 0.00223 22.87289 -1.50E-02 27.29408 9.742109 1081.595 -0.08777 94.42371 0.127618 109.4191 0.54998 971.2312 9.847706 494.9556 -0.00953 203.2434 -0.0913 190.6168 -0.06848 198.519 8.015444 341.0624 0.01983 145.6926 -0.06997 123.7691 -0.01921 131.7508 8.809187 813.968 0.176202 65.68875 0.11197 70.61679 -0.28905 743.6734 7.002635 586.8246 0.156424 33.36041 -0.02227 35.93929 0.04767 40.14169 5.790843 443.7699 0.012476 35.34626 -0.02541 18.22906 0.052648 23.89381

from level 3 v. mean3 var3 62.60113 22983.61 -2.45283 7666.587 4.693387 10103.26 -0.49866 4089.01 15.8225 1201.232 0.769347 542.9973 0.18852 430.636 -0.425699 445.3272 14.08097 1024.546 0.447561 423.5394 0.299218 381.2967 0.167338 366.5081 44.95844 13564.05 -1.491764 5455.962 -2.631746 10964.7 -1.300389 2642.356 10.23388 522.1415 0.512183 205.1914 0.347524 166.8923 0.67664 231.9094 8.613727 405.4583 0.252421 134.506 0.291857 173.8282 0.424928 295.4322 64.84538 36861.13 -2.397022 11381.52 0.833907 5807.139 11.73401 24472.83 15.36195 1147.539 -0.141222 513.7979 0.361817 427.6713 -0.240363 435.2458 13.25566 879.4641 -0.068546 386.5766 0.096121 322.4603 -1.76E-01 341.6824 73.16934 38910.87 0.430619 9465.986 -0.944108 3896.089 -4.278327 32008.63 46.32368 19414.54 1.114004 197.5954 -0.12789 174.7708 0.252212 163.0227 34.83047 13525.36 0.093707 133.2343 -0.058186 91.33412 0.794429 213.286


features


from den. QRS RMS 5350 1326 4920 664.8 4320 666.7 5400 591.1 8418 66 7824 24.66 8580 23.48 8520 24.47 8357 77.93 8335 21.65 8444 20.12 8358 42.61 5562 1035 3133 548 3850 519 5021 470.7 8216 95.81 7602 6.155 7413 16.98 8070 62.96 6523 560 7408 4.504 7474 10.52 7659 65.77 5100 4767 4080 2265 5760 578.6 3960 2680 8088 82.95 7920 25.74 8280 22.07 7020 129.9 7974 100.3 7791 23.25 8163 23.47 7626 112.9 5331 4051 3625 1998 4388 671.2 5317 2052 8077 61.03 7477 7.787 7592 5.789 7820 83.87 7973 65.55 7202 5.349 7507 17 7677 86.59

from level 1 v. mean1 var1 0.887321 9.346517 -4.22E-05 8.281516 3.36E-03 0.200594 -1.50E-03 1.688251 2.374008 30.33548 -0.0136 14.77524 3.99E-03 11.13579 0.006288 10.19284 1.97768 21.74701 -0.00646 9.97361 0.003996 7.890589 0.003941 7.650738 0.442336 2.629875 0.006767 2.320047 0.003506 0.268395 -2.12E-03 0.276583 0.771649 3.90515 -0.00897 1.635289 0.008254 1.239122 -2.77E-04 1.384681 0.458947 2.152462 -4.99E-03 0.846652 0.004859 0.828405 -4.67E-03 0.980278 1.062762 9.118798 6.09E-03 0.399752 -0.06957 6.004033 -0.00247 2.632536 2.369835 30.2155 -1.30E-02 14.74064 0.004614 10.7214 0.00559 9.274888 1.981132 21.93552 -4.15E-03 1.02E+01 5.93E-03 7.76E+00 -0.00128 7.674528 0.778481 5.202028 0.002716 0.551882 0.004857 3.001266 -0.01748 2.284233 0.743376 3.611919 -0.0033 1.525278 0.007103 1.198091 0.001549 1.49285 0.624117 2.630747 -0.00634 0.973982 3.59E-03 0.801052 -2.83E-03 1.098493

322

from level 2 v. mean2 var2 5.456894 344.883 -0.02771 293.8899 0.115875 52.72611 -0.14021 44.37145 9.822398 491.1449 0.004739 203.7361 -0.09519 191.4293 0.016896 193.6726 7.989306 339.0866 0.015574 143.4351 -0.05965 125.7225 0.035813 132.7093 3.96186 174.7261 0.052602 143.3097 0.081689 31.35609 -0.10925 23.84434 4.244686 107.7339 0.032885 51.20549 -0.00271 31.5617 0.024523 33.44785 3.400011 111.2251 0.00797 28.70321 -0.01738 20.84872 0.007213 26.2797 11.85327 1057.698 0.119654 104.2378 -0.22247 431.0497 -0.08248 641.5811 9.810117 487.8671 0.011005 203.5767 -0.08436 180.0917 -0.23023 181.4398 7.988486 339.2772 0.027572 144.9224 -0.06354 123.8858 -0.00429 128.8866 9.111274 690.4704 0.060862 70.17419 0.05163 305.959 0.020596 408.0857 4.222315 103.1254 -0.00227 47.80233 0.025404 28.8994 0.047985 43.33738 3.383485 66.7724 0.026134 28.51692 -0.03003 22.59077 -0.00143 25.86421

from level 3 v. mean3 var3 33.42201 8291.756 -0.262632 4613.947 0.812564 2676.676 -1.58159 3490.294 15.87755 1215.033 -0.012597 508.5528 0.297417 434.873 -0.251452 456.7968 13.17154 872.87 -0.046572 376.8682 0.17871 318.3681 0.204705 329.5516 27.48026 5698.43 0.256508 3034.866 0.627703 1808.639 -1.200674 2516.104 10.27128 770.9384 0.148613 164.4981 -0.347945 125.9294 0.787925 194.5915 17.53221 2943.112 0.078401 123.5891 -0.155978 90.39532 0.269769 184.8155 54.31091 22875.87 0.632977 5500.647 4.75368 4837.175 2.633396 16094.82 15.40128 1153.699 0.108422 503.9163 0.434954 379.2696 -0.517532 467.8766 13.34614 899.6225 -0.005745 384.5638 0.159291 345.9796 0.17333 350.6023 43.42711 16115.5 0.468324 4186.41 -0.239093 5165.676 3.82812 9572.051 9.473885 486.571 0.069518 201.609 0.111741 139.6243 0.516491 193.3157 7.804747 321.1233 0.091268 107.1318 -0.234281 163.4938 0.163844 131.1075


features


from den. QRS RMS 4612 2154 4680 1327 4972 389.5 4620 717.2 7552 60.88 7560 24.77 7924 23.27 7740 23.05 7443 59.88 7454 22.78 7940 20.72 7579 25.35 4838 1776 3628 1253 2142 319.4 4583 599.7 7822 16.56 7572 6.089 7029 5.787 7593 15.77 7566 20.13 7297 30.9 6646 4.671 7157 25.65 3648 3326 2916 1485 5016 838.4 2640 1456 7428 61.19 6696 24.93 7500 24.35 6420 28.05 7325 55.22 6567 21.87 7385 21.87 6561 22.95 3723 2797 3024 1260 4014 758.6 2650 1245 7471 18.54 6572 6.85 6745 7.179 6576 11.28 7360 18.9 6536 9.511 7114 6.247 6358 9.603

from level 1 v. mean1 var1 0.838459 7.322859 -0.00552 7.54568 0.001681 0.171848 -0.00475 0.30785 2.380481 30.50358 -1.31E-02 14.73169 0.002889 11.09304 0.006442 10.4764 1.982752 21.99152 -0.00323 9.956656 0.003398 7.838143 3.75E-03 7.929457 0.501252 2.172656 0.014374 1.903149 0.001686 0.206279 0.001007 0.354892 0.768782 3.74787 -0.003 1.645628 0.006255 1.208 1.19E-04 1.466411 0.575907 2.25448 -0.00541 0.831898 0.001586 0.89356 -3.24E-03 0.838595 0.445194 1.379353 1.48E-02 0.725984 0.010455 0.59616 -0.002 0.27397 2.379797 30.47214 -1.35E-02 14.70952 0.003575 11.0618 4.23E-03 10.23123 1.979555 2.19E+01 -3.67E-03 9.95E+00 0.003987 8.092244 8.08E-03 7.59E+00 0.432956 1.21189 0.010991 0.606409 -0.00387 0.474863 -0.00497 0.314182 0.83093 4.205523 -0.00874 1.46316 0.007187 1.660227 0.000101 1.548107 0.63167 2.633781 -0.00238 0.918196 0.003385 0.995912 -7.04E-04 1.084482

323

from level 2 v. mean2 var2 6.642642 302.55 0.091932 236.8751 0.11211 38.51162 -0.10765 68.82718 9.829032 492.3841 0.010803 201.8367 -0.10819 190.4413 0.016254 198.153 8.002616 341.1838 0.029301 144.6633 -0.05469 123.5881 0.014713 136.8437 4.677878 158.7817 0.105821 128.9261 0.029847 18.72524 -0.03231 37.05579 4.128997 95.42001 0.008269 43.01861 -0.01973 32.72346 0.00253 36.41002 3.148215 58.8564 -0.00105 29.72216 -0.0133 19.70799 -0.00264 22.83052 6.956286 263.1456 0.159739 154.6763 -0.11879 76.43171 -0.09057 66.50544 9.829071 493.8257 -0.00043 201.9999 -0.08811 190.1925 -0.0007 194.3548 7.962978 337.6783 0.037978 139.6635 -0.06436 128.5568 -0.0074 131.1597 5.135732 154.4455 1.20E-01 77.96627 -0.03972 62.68809 -6.99E-02 40.74651 4.503921 115.3077 0.032232 49.77146 -0.02787 43.4801 0.001491 40.54841 3.426632 68.65279 0.037475 28.17517 -0.01386 26.39792 -0.0008 25.24242

from level 3 v. mean3 var3 39.15916 11167.97 -2.471993 7524.079 -0.878225 1726.691 1.151383 3172.349 15.50933 1156.802 0.101307 503.1589 0.173284 410.5529 -0.153991 441.8977 13.19043 870.9563 0.093099 384.2432 0.113317 333.7273 -0.092627 316.9682 32.85843 8075.804 0.388081 6328.363 0.196891 1156.497 1.067146 2200.231 8.434066 355.1893 0.102584 142.2914 -0.048806 122.9431 0.262977 163.9784 6.984555 253.2812 0.090544 221.9513 0.097057 95.66752 0.323404 101.5129 55.73622 18364.52 0.680783 5367.91 -4.960653 8179.483 -0.516731 6051.226 15.65891 1184.552 -0.060079 503.53 0.382442 421.3776 0.428542 487.391 13.09723 858.6006 0.108268 374.9126 0.101773 325.4149 0.129345 339.1843 48.38418 14171.62 0.662337 3907.789 0.332291 7723.643 -0.083244 4874.791 9.437916 443.0801 0.233162 170.04 -0.292988 163.0499 0.225366 211.5449 7.988399 334.0878 0.335631 129.8379 -0.017104 138.3616 0.097971 134.054


features


from den. QRS RMS 6060 2773 4680 2589 5040 2779 13992 177 11460 68.59 8700 24.64 8640 23.26 8630 32.27 11346 105.8 11323 21.25 8524 19.69 8476 58.28 6118 2379 3920 2294 4541 2644 6096 1125 6049 2446 7675 6.609 8477 5.6 8224 147.5 6278 2217 8526 5.067 8259 4.138 8072 168.2 4640 2846 4140 960.3 4980 809 3986 1557 7920 63.47 7080 22.95 7618 24.27 7080 32.29 7816 66.85 7129 21.74 7895 21.89 7700 44.29 4772 2368 3523 781.6 4261 730.1 4058 1348 7844 30.83 7049 15.17 7075 25.23 7737 31.99 6672 589.8 7000 4.749 7328 6.509 6708 53.69

from level 1 v. mean1 var1 0.746386 5.124975 -0.00818 0.990259 5.26E-03 3.64809 -0.00565 0.660992 2.36997 30.23128 -0.01303 14.69837 0.003746 10.954 0.001913 10.32376 1.972347 21.72727 -0.00551 9.864308 5.11E-03 7.70E+00 0.004735 7.927237 0.593739 3.437843 -0.00584 1.146453 0.005872 3.335515 -0.02729 2.772217 0.669932 3.813103 -8.16E-03 1.424904 0.006688 1.28705 9.01E-03 1.363329 0.666079 3.666971 -0.00355 1.04435 0.002307 0.861118 0.00381 1.212474 0.701441 3.40333 0.007111 2.313528 -0.01098 1.113892 0.013212 0.429959 2.374128 30.30877 -0.0136 13.51065 0.008151 10.92673 0.01499 10.32313 1.98197 2.19E+01 -0.00561 9.94E+00 0.004392 7.79E+00 7.49E-03 7.82E+00 0.629078 2.824113 0.004184 2.006449 1.13E-03 0.769156 0.009503 0.504182 0.775547 4.008743 -0.00601 1.431194 0.007688 1.378279 0.002738 1.715056 0.571291 2.550681 -0.00619 1.070587 0.002875 0.779022 -0.0032 1.10035

324

from level 2 v. mean2 var2 9.128791 790.5123 -0.14163 245.7328 2.42E-01 917.5824 -0.04507 88.90548 9.901356 499.8545 0.011384 203.1412 -0.08903 187.8439 0.033455 208.5108 7.970407 339.3243 0.022225 139.532 -0.05638 121.1054 0.053311 141.9766 7.145929 535.4425 -0.06507 176.7781 0.003363 772.3122 0.108843 439.1372 7.991108 582.2974 0.030435 48.3323 -0.02626 35.35806 0.178494 40.02248 7.251142 484.8845 0.007987 35.08995 0.008833 19.51401 -0.01065 36.50425 9.748838 628.6664 0.075367 464.2608 -0.33912 122.4118 0.365808 115.9299 9.834611 493.743 0.120777 197.2545 -0.09387 188.6195 -0.01264 199.6066 7.977452 339.5673 0.028246 142.0253 -0.06162 122.6937 -0.01008 134.3951 7.709584 412.5378 0.055346 301.2818 -0.06432 100.0326 0.292867 71.36926 4.178118 102.1153 0.035237 45.68955 -0.01074 36.51355 0.022027 41.07309 4.363295 162.6349 0.036862 29.35535 0.001672 21.08293 0.011748 30.06717

from level 3 v. mean3 var3 51.25195 21255.62 -0.662224 11366.49 -1.604495 38849.76 0.422371 1594.309 16.78985 1388.077 0.036096 509.4381 0.398494 432.7297 -0.751574 599.0176 14.23165 1060.511 0.014912 373.5288 0.154375 325.7083 0.163473 496.3051 43.65084 16387.31 -0.306987 9134.453 0.029638 34598.31 2.621198 9042.504 46.36422 16695.6 0.183314 187.7594 -0.167374 147.036 2.209346 601.3823 40.83556 14527.42 0.062785 121.2137 0.202891 79.79045 0.140184 877.8041 56.86776 19266.28 -1.112363 9226.541 1.148341 6583.331 3.91951 5417.449 15.71211 1189.874 0.443022 500.3221 0.49311 395.4608 0.263022 502.5653 13.48912 910.1754 0.092262 377.6107 0.161096 353.0254 0.265484 353.0631 47.38901 13824.23 -0.863248 6754.281 -1.016012 5631.792 2.588153 3555.209 8.940664 400.2303 0.171702 164.2156 -0.127092 241.6961 0.402052 175.8866 18.56733 4188.173 0.190403 118.6022 0.318346 129.307 0.339347 163.5777


features


from den. QRS RMS 6480 2796 5160 1611 4968 1052 6480 872.8 9240 69.67 9180 24.6 9120 22.38 9120 35.85 9117 70.93 9054 22.11 9176 20.15 9202 34.5 6623 2084 4052 1408 5052 836.7 6622 568.3 9017 79.9 8580 5.527 8710 5.412 8945 36.36 8966 38.57 8441 4.956 8972 4.878 9060 29.97 3876 6494 2858 1503 3660 520 3900 5434 6936 66.13 6458 24.8 6840 23.77 6840 44.95 6828 91.69 7193 22.49 6719 26.1 6740 74.3 3846 5755 2913 1279 3203 356.4 3837 4935 6401 974.5 6414 8.046 6184 8.273 6656 62.51 6712 66.46 6226 4.508 6124 11.17 6482 100.2

from level 1 v. mean1 var1 0.570106 2.652435 -0.00392 1.133491 0.010618 1.550863 0.009225 0.678609 2.372945 30.27339 -0.01347 14.72121 0.016586 10.65664 0.031624 10.11338 1.956522 21.53502 -0.00476 10.14873 0.005234 7.597547 0.002912 7.553354 0.477093 1.974881 1.89E-02 0.958678 0.002196 0.983461 4.22E-03 0.512307 0.708896 3.279409 -0.00555 1.487216 0.008279 1.046581 -0.00083 1.360751 0.57372 2.240797 -0.00929 0.853315 0.003715 0.799037 0.002837 1.102457 0.882432 7.490631 7.09E-04 0.974392 8.28E-03 2.67774 -0.01562 4.632918 2.380905 30.51558 -1.27E-02 14.69762 4.30E-03 11.07964 0.018547 10.37185 1.992329 2.22E+01 -5.98E-03 1.03E+01 3.81E-03 7.82E+00 1.01E-02 7.86E+00 0.871712 6.278233 0.002555 0.898854 0.001766 2.014894 -7.40E-03 4.072243 0.778805 4.10966 -5.31E-03 1.660216 0.005154 0.956842 0.003547 1.543256 0.603389 2.465911 -0.00524 0.775988 0.000274 0.692869 -0.00314 1.253118

325

from level 2 v. mean2 var2 8.060486 527.2423 -0.15905 279.9895 0.045577 279.8451 0.038843 132.3108 9.793907 483.9301 0.001546 202.9623 -0.01482 181.6888 0.144869 196.0338 7.997195 340.4438 0.020453 143.9659 -0.05771 122.189 0.010241 137.7339 6.085128 358.2065 0.117904 182.2237 -0.05856 200.414 -0.16677 59.9992 4.024425 96.18511 0.004096 41.54868 -0.0006 28.70336 0.042104 37.37734 3.367627 67.93565 0.012425 32.27655 -0.02828 20.55145 0.024893 31.03258 14.74394 1772.983 0.062679 212.8923 -0.0291 618.4932 0.478988 1162.151 9.850375 493.2214 0.008989 203.4059 -0.08454 189.8824 0.073626 197.3597 8.041183 342.9739 0.031384 145.3468 -0.07695 123.5809 0.023091 136.498 12.45283 1341.891 0.04938 131.0903 -0.02103 383.1236 0.409832 976.8517 5.384681 304.1724 0.025227 58.90833 -0.02298 25.70242 0.036353 37.91435 3.330279 63.71989 0.032608 25.53832 -0.03018 17.64183 0.022756 30.20474

from level 3 v. mean3 var3 56.63873 27833.82 0.29645 16788.92 -1.127518 17334.39 -3.315179 2821.036 15.54394 1190.677 -0.014069 508.2532 -0.204419 425.8304 0.192909 629.3443 13.97101 1031.917 -0.014783 380.0996 0.210564 316.8855 -0.157499 474.6603 46.15949 20429.99 0.509688 12839.56 -1.59189 13030.48 -2.909868 1698.027 10.50892 973.3427 0.081627 139.4654 -0.054972 137.8422 1.499124 381.6805 9.152654 516.4527 0.082423 114.8753 0.017437 106.9895 0.233781 320.2062 97.57789 81384.5 0.901767 8581.954 0.261691 15891.87 6.47E+00 66413.12 15.69452 1192.916 0.019083 512.5912 0.371062 424.2321 0.521061 516.4855 13.2998 886.0613 0.147243 387.5801 -0.054479 319.0534 0.4911 387 87.09557 67646.59 0.878235 6555.157 0.415236 10392.54 5.701658 58405.56 20.36783 11525.97 0.298141 222.3781 -0.397661 137.5352 0.779092 241.7615 7.75802 315.176 0.182916 114.7843 -0.190182 104.3329 0.800913 164.8713


features


from den. QRS RMS 4080 2749 3564 779.6 2804 818.4 4080 1634 6900 144.6 6300 29.44 6464 22.28 6780 169.8 6795 175.2 6163 27.17 6510 20.64 6712 181.1 4066 2268 2543 635.4 2835 631.8 4097 1396 6781 124.5 6192 10.87 6487 6.426 6532 200.5 6557 203.9 5359 181.8 6332 5.04 6496 195.1 5388 1702 5280 654.6 3840 801.4 4774 672.7 7848 61.86 7740 25.52 8038 23.64 7920 23.31 10699 59.18 10373 22.81 10736 20.26 7774 25.54 4755 1433 3546 570.6 3881 637.1 4808 533.2 7668 23.27 7622 6.323 7762 5.72 7445 19.37 7454 86.72 6987 6.01 7742 4.79 7487 17.81

from level 1 v. mean1 var1 0.528517 2.546796 -2.68E-03 0.320634 -0.00425 1.418553 -0.02177 1.134584 2.384528 30.44744 -1.39E-02 14.74894 0.015792 10.6467 0.011298 10.28129 1.973036 21.7697 -0.00639 1.00E+01 0.005939 7.88E+00 0.005561 7.62E+00 0.560308 2.343349 0.005325 0.372273 -2.18E-03 1.257748 -0.01387 1.003503 0.779996 3.903982 -0.00652 1.409423 9.65E-03 1.418678 -0.00276 1.661538 0.577274 2.342858 0.000999 0.694863 0.002435 0.71933 -2.51E-03 1.181887 1.062995 13.00533 -1.20E-03 3.17107 -0.00092 0.261778 -0.00858 10.95818 2.372067 30.26116 -1.36E-02 14.64937 0.008048 10.93617 0.006116 10.45216 1.983764 21.96455 -0.00725 9.90E+00 0.004694 7.85443 0.003546 7.902376 0.510046 2.361895 -0.00057 0.51056 1.78E-03 0.28444 -0.00297 1.856554 0.74823 3.617139 -0.00641 1.253166 5.33E-03 1.335406 -0.00057 1.522072 0.577228 2.357165 -0.00456 0.711011 3.87E-03 0.843177 -6.43E-05 1.146087

326

from level 2 v. mean2 var2 9.066514 598.2292 -0.03831 76.41285 -0.01062 364.8969 -0.41942 250.5257 9.85926 494.9079 0.015462 202.7254 -0.04361 185.0536 -0.03392 202.7274 7.941309 334.9142 0.030153 141.37 -0.05821 122.8315 -0.01579 133.4564 7.310301 392.1902 0.023378 47.52792 0.000436 247.0338 -0.30717 150.6659 4.323975 107.6683 0.016464 45.37738 -0.00351 38.69838 -0.02032 44.09723 3.283485 65.95865 0.036555 39.33515 -0.02688 19.03077 -0.02476 31.54769 5.613808 264.9818 -0.09276 85.35256 0.011763 74.19765 0.097085 161.6248 9.751051 486.3506 -0.00356 199.6034 -0.07389 187.859 0.013018 195.5422 7.959416 337.7227 0.025975 140.616 -0.05577 123.9973 0.018142 135.458 4.090753 111.3229 0.029887 26.15864 0.01538 43.4459 0.053771 58.00026 4.122921 99.70253 0.04743 43.10719 -0.0192 35.80442 -2.89E-04 39.25732 3.243555 62.9471 0.020559 24.6348 -0.02349 21.63672 0.016736 26.66951

from level 3 v. mean3 var3 58.93133 25528.37 0.34485 4631.411 0.23675 20385.33 0.762283 4446.981 16.22757 1317.485 0.343563 507.9975 -0.298185 440.4017 1.30051 653.8167 13.78951 971.5761 0.217746 379.6446 0.109521 322.1018 0.776873 484.625 50.44162 18948.52 0.741547 3473.696 0.164236 15336.51 0.419472 3030.766 9.41853 488.2787 0.283717 145.1287 -0.101225 146.5176 -0.017929 372.8038 8.569093 429.0282 -0.536998 804.8421 -0.061771 120.6621 0.06921 262.3195 27.66814 6147.785 -1.399241 985.6702 0.123407 4248.755 1.271435 3057.93 15.524 1161.245 0.165405 512.7549 0.543319 444.5377 -0.155753 419.9483 13.07254 859.3259 0.210563 382.84 0.211248 325.7186 -0.091133 314.1629 27.46136 4672.176 0.370381 748.8134 -0.031654 2816.019 0.862224 1980.955 8.5871 367.6187 0.420577 155.4544 -0.053363 145.1119 0.348788 144.5728 8.30505 473.2656 0.241225 104.5413 0.097908 117.3774 0.230182 108.0717


features


from den. QRS RMS 3930 5743 3960 2931 4320 965.2 3960 2889 7380 60.73 7560 25.71 7380 23.3 7260 25.08 7278 62.88 7429 24.71 7682 20.89 7340 25.71 4101 5016 4027 2602 3980 775.9 4161 2558 7404 18.27 7369 8.559 7146 9.497 7101 27.09 6854 719.2 7257 9.612 7108 5.238 6925 74.87 7292 2218 7388 485.3 7694 1232 7416 823.2 10260 68.29 10380 25.49 10680 25.22 10260 37.15 10158 71.77 10790 23.49 10572 23.75 10318 33.39 4659 1701 4336 354.2 3629 1244 4533 547.5 7364 34.08 7101 9.137 7139 10.5 6381 38.23 7351 36.87 7004 7.767 7023 9.87 6954 33.49

from level 1 v. mean1 var1 1.028761 9.623982 -0.0102 2.955679 7.50E-05 1.859092 1.28E-02 5.842252 2.384478 30.57712 -0.01372 14.82251 3.92E-03 11.09285 1.26E-02 10.31548 1.994697 22.22612 -6.64E-03 1.01E+01 4.66E-03 8.02E+00 3.81E-03 7.97E+00 0.948516 7.681122 -0.00546 2.135934 7.51E-04 1.568308 0.006681 4.856461 0.82932 4.288155 -4.12E-03 1.485662 5.56E-03 1.437912 0.003211 1.898219 0.67397 3.542176 -0.00342 1.201794 0.005523 0.914826 -0.00029 1.090561 0.352633 1.164532 -0.01904 0.438583 -0.00297 0.592875 8.64E-03 0.250431 2.379276 30.48655 -0.01281 14.73617 0.004904 11.05794 1.54E-02 10.31859 1.988085 22.07108 -0.00163 9.46E+00 0.003442 8.04E+00 4.83E-03 7.98E+00 0.378798 1.153693 -0.01273 0.41832 -0.00312 0.631992 6.16E-03 0.309743 0.777188 3.814283 -0.00848 1.284287 0.007472 1.593807 0.016075 1.119794 0.62271 2.607523 -4.92E-03 0.799367 0.003545 1.002987 -0.00107 1.158589

327

from level 2 v. mean2 var2 15.49856 1875.887 -0.07496 449.0022 9.75E-02 384.7628 0.156173 1280.203 9.849133 494.614 0.00131 204.0025 -0.09631 190.3404 -0.04842 197.3091 8.023945 342.9521 0.009647 143.5211 -0.05474 126.5603 0.006686 135.8407 12.84389 1351.827 -0.02318 316.9062 0.027155 250.1216 0.008435 949.5084 4.395455 108.7449 0.019388 44.26538 -0.01154 36.07008 0.07054 45.55404 4.592274 242.1445 0.014156 35.67455 -0.01238 24.30258 0.043696 29.60376 5.936667 266.8341 -0.17904 96.48066 -0.04733 139.3843 1.94E-01 65.70421 9.850008 493.4403 0.015828 203.6996 -0.07721 189.2197 0.00511 197.2157 8.009531 341.7848 0.024157 139.9453 -0.05052 128.5676 0.023686 136.667 4.467248 151.9833 -0.10791 47.87144 -0.02799 93.38233 0.174806 40.63369 4.204617 101.8091 0.043492 43.31188 0.010463 40.45862 -0.03415 30.19107 3.374489 67.38384 0.031395 26.61998 -0.00928 25.91499 -0.02339 26.43172

from level 3 v. mean3 var3 78.40626 39374.51 1.026889 14984.82 -0.1523 7663.433 -3.919078 22580.17 15.30398 1137.582 0.017361 509.6533 0.251378 422.0933 -0.285722 429.6934 13.34821 891.6798 -0.126799 382.5206 0.169722 333.8314 -0.299411 336.3346 68.44052 30776.99 0.831163 12438.48 -0.350862 5512.973 -4.134474 17532.1 8.88643 402.1329 0.025803 178.8278 -0.13361 164.4381 0.505634 167.3742 14.01254 3596.112 -0.009495 143.6993 0.085696 120.9111 0.77602 223.5454 42.41143 11473.28 1.788852 2722.693 -2.589324 6429.072 3.890664 4092.718 15.42146 1154.683 0.166096 512.6482 0.563976 444.2259 0.406992 434.1285 13.20522 875.4176 0.210906 375.608 0.456385 347.411 0.16623 317.8369 35.11903 8089.926 1.271286 1678.36 1.288546 5361.657 3.116431 2834.687 8.879079 399.5021 0.542527 156.5987 0.329102 159.136 -0.463333 194.9643 7.868925 316.424 0.407592 121.4869 0.314329 148.6088 0.044556 160.0292


features


from den. QRS RMS 5100 3505 5220 2560 5114 1068 4740 720.6 7860 80.2 8220 24.66 8008 36.16 7920 23.19 7758 80.08 8104 22.08 7830 44.66 11183 23.04 5157 3007 2849 2708 5355 881.7 4088 1865 7565 85.07 6852 19.18 7876 31.89 7629 10.77 6544 842.9 6758 4.76 4883 665.2 7335 19.47 5122 2710 5220 1623 4200 758.5 4482 1211 7680 63.6 7740 25.45 7620 23.39 7560 34.71 7581 82.22 7754 23.51 7495 25.55 7600 42.31 4559 2618 3140 1485 3737 593.4 4527 984.8 7603 31.46 6649 6.658 6935 5.943 7325 63.66 7507 55.07 6655 7.377 6840 14.4 7241 79.63

from level 1 v. mean1 var1 0.623827 2.774093 -4.21E-03 0.409831 -0.00408 1.578437 1.51E-02 2.65761 2.394731 30.63732 -1.25E-02 14.71241 0.011257 11.22842 5.36E-03 10.55745 1.999439 22.30866 -5.15E-03 10.06492 4.55E-03 8.03E+00 0.003819 8.006554 0.513341 2.222921 1.87E-02 0.528146 -0.02559 0.730923 -0.00663 3.087512 0.723839 3.727241 -0.007 1.498684 0.008996 1.415921 0.001902 1.70042 0.548482 2.413079 -0.00637 1.136092 -0.00411 0.880985 -0.00289 1.090731 0.378881 1.664709 -2.20E-03 0.18083 0.009857 1.306363 0.003382 0.372598 2.381308 30.56363 -0.01314 14.74304 0.003544 11.12813 0.017155 10.32577 2.014489 22.60773 -0.00323 9.721184 0.003635 8.199715 5.35E-03 8.13E+00 0.391765 1.045161 0.006982 0.321634 0.007654 0.481593 0.00139 0.409477 0.793674 4.088968 -7.52E-03 1.245733 0.008415 1.279443 1.34E-03 2.014337 0.626436 2.619107 -1.87E-03 1.04666 -0.00042 0.745589 0.00187 1.139157

328

from level 2 v. mean2 var2 7.981768 507.7559 -0.10978 138.1893 -0.61938 210.472 -0.52102 394.6735 9.915269 494.174 1.19E-02 203.1791 -0.1527 189.4258 0.00357 199.6597 8.09828 348.2414 0.021579 145.6235 -7.19E-02 130.0342 0.015239 137.2558 6.60689 372.9926 0.136784 109.5593 -0.64043 146.1219 -0.39472 546.7014 3.974969 96.68352 0.030135 46.02857 0.014643 35.75586 0.007038 39.57945 4.055796 131.1479 0.035098 31.07454 0.023411 102.7074 0.010348 29.36999 5.25733 210.9972 -0.07536 56.65567 0.151564 98.72683 0.062852 94.8899 9.835415 493.0766 -0.00851 203.1587 -0.08554 191.6258 0.028827 195.3999 8.124637 351.4941 0.018567 146.2751 -0.06995 129.6683 3.89E-02 140.4496 4.560996 133.1214 0.056856 55.92564 0.094079 45.3901 0.068612 55.49683 4.357332 108.5208 0.050691 40.85358 -0.00507 35.14447 0.08643 49.36613 3.383052 68.39003 0.038129 33.06948 -0.07486 19.74207 0.023513 26.38763

from level 3 v. mean3 var3 58.12114 27368.45 -0.033184 13974.13 -4.167132 13238.45 -2.080902 4515.969 15.04659 1109.368 0.021734 508.5122 -0.239053 370.6526 -0.276427 431.2113 13.65489 948.048 0.033266 384.8982 -0.09232 407.5795 -0.151366 323.1417 49.87227 20818.64 1.711888 12090.72 -1.713651 8736.799 -4.0438 15856.55 8.985821 630.2927 0.061006 205.7308 -0.304183 150.3602 0.140975 137.5294 19.71796 5684.655 0.144124 125.5988 3.018498 5239.978 0.231308 139.58 41.19724 12155.8 -2.875164 7430.33 1.429986 3368.405 2.15515 4156.208 15.24392 1139.314 -0.161994 510.914 0.589712 447.2163 0.116985 421.4649 13.53857 928.4799 0.048632 386.9978 0.105501 351.7804 0.189452 371.2909 41.86905 10220.57 1.054954 7130.015 1.043968 2390.557 2.158176 2838.327 9.04467 420.2637 0.166653 157.0274 0.068063 164.5507 1.202436 220.8368 7.568666 331.8742 0.209443 113.1134 -0.271427 103.4054 0.472435 233.3342


features


from den. QRS RMS 5160 3273 4844 1312 4980 1360 5160 1037 8040 67.59 8024 24.66 8100 23.58 8160 25.22 7940 69.03 7979 21.62 8432 21.43 8003 34.07 5196 2715 3252 1204 4228 1142 4746 883.5 7107 464.1 7381 5.42 7413 7.41 7667 34.72 5888 1566 7660 4.379 7342 6.176 6944 43.24 5478 1899 5540 1161 6060 246.8 5538 614 8718 59.48 8820 24.7 8640 23.27 8616 23.32 8611 53.55 8731 21.59 8522 20.58 8573 21.64 5495 1654 3916 1262 4509 730.6 5502 591.9 8534 19.36 8343 6.491 8458 5.932 8390 10.25 8257 86.73 7668 4.453 8387 4.933 7156 17.65

from level 1 v. mean1 var1 0.452094 2.54338 -5.97E-04 0.386438 0.003796 2.186687 0.013504 0.425814 2.379095 30.48537 -0.01341 14.76121 0.003833 11.14977 9.75E-03 10.36961 1.990517 22.13602 -6.50E-03 9.99E+00 0.004255 7.981851 0.003453 7.749675 0.502367 2.584066 0.007409 0.393621 8.15E-04 2.10951 0.009563 0.613843 0.617618 2.887142 -9.10E-03 1.319987 0.008078 1.454498 0.0021 1.620945 0.464619 1.940948 -0.0047 0.828292 0.002889 1.001019 1.14E-02 0.65574 1.928226 50.09123 0.017127 34.83547 -1.94E-03 1.877737 -0.01483 16.70592 2.37054 30.23646 -0.01359 14.70107 0.003387 10.93421 0.015963 10.19047 1.971021 21.79371 -0.00639 10.00672 0.003765 7.966481 0.006609 7.49344 1.232292 20.41685 0.004817 14.43935 0.006005 1.118014 -0.00739 6.88981 0.760075 3.651358 -0.0038 1.389247 0.006628 1.495856 -0.00023 1.383355 0.583058 2.950744 -5.49E-03 0.891313 0.004223 0.94955 0.000428 0.76546

329

from level 2 v. mean2 var2 8.443745 729.1814 0.158005 72.28222 -0.31285 620.4608 0.383605 146.7838 9.823549 491.0398 0.007248 203.2961 -0.09355 189.8976 0.057212 195.3952 8.023447 341.7456 0.019482 142.5619 -0.05758 126.8589 0.019481 133.3723 7.018231 548.7023 0.038111 38.71899 -0.09906 492.9673 3.05E-01 114.0796 4.003393 131.2182 0.032733 42.65661 0.004321 36.04632 0.00181 40.94103 4.656777 246.9965 0.020219 27.81933 -0.01925 24.8466 -0.03858 16.84226 11.22502 1173.431 0.22099 829.7725 0.117973 137.6654 -2.92E-01 320.3382 9.789421 489.3298 -0.00728 203.0054 -0.08866 187.4149 -0.00468 194.8625 7.940149 336.6848 0.021777 141.1806 -0.05994 126.401 -0.0006 131.2712 8.833195 749.9436 0.067846 530.8683 0.098953 142.0253 -0.15828 232.1923 4.220572 105.1691 0.006812 46.71712 -0.00376 39.59508 0.012889 38.64952 3.231008 81.06066 0.030214 25.18356 -0.029 23.49032 -0.00727 20.72628

from level 3 v. mean3 var3 64.87112 43361.63 -0.480947 3717.374 -3.607309 38969.15 -0.796341 13646.21 15.73735 1196.468 0.070706 507.9108 0.316504 428.8305 0.029445 457.5778 13.25381 884.2048 -0.002474 377.8457 0.225126 344.1885 0.04003 322.8125 56.16832 34495.82 -0.057913 3011.25 -1.010641 32083.81 -0.934231 10793.87 14.96798 4654.399 0.13371 154.7625 0.121309 156.5534 0.081532 186.2416 31.59893 14879.04 0.091626 120.8577 0.22549 100.878 -0.185781 120.6319 52.19179 20682.14 -0.502555 10562.74 0.743544 4637.996 -2.873363 7321.912 15.36766 1146.061 -0.128873 508.6908 0.391255 423.7787 0.007219 438.3839 13.04438 853.8581 -0.031581 374.7588 0.190467 325.7752 0.020507 325.787 44.68924 15291.92 0.324108 8371.969 -1.121826 6909.63 -1.947244 5657.099 8.910281 401.7369 0.055232 173.1566 -0.059287 139.7072 0.210411 176.089 8.942887 925.2236 0.141085 95.89407 0.059308 128.2514 0.161578 116.481

Vita

VITA Candidate’s full name: Alberto Taboada Crispí Universities attended: Universidad Central de Las Villas, Cuba, 1980-85, B.Sc. (Electronic Engineer) Universidad Central de Las Villas, Cuba, 1996-97, M.Sc. (Electronics) University of New Brunswick, Canada, 1997-2001, Ph.D. Publications: 1. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Procedure to detect ventricular late potentials (in Spanish),” Invention Patent Application, No. 165, OCPI, Cuba, October 1999. 2. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Adaptive line enhancing plus modified signal averaging for ventricular late potential detection,” Electronics Letters, Vol. 35, No. 16, pp. 1293-1295, August 1999. 3. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Rubén Orozco Morales, “Evaluation of alignment algorithms to detect ventricular late potentials (in Spanish),” Ingeniería Electrónica, Automática y Comunicaciones, Vol. 20, No. 4, pp. 54-60, 1999. 4. Alberto Taboada Crispí, Gustavo Grillo Ortega, and Diosdado Hernández, “Data Acquisition System for Welding Processes: CISDAT-PC-01 (in Spanish),” Construcción de Maquinarias, Cuba, Vol. 23, pp. 2-3, 1992. Conference Presentations: 1. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Flexible Analysis Station for Ventricular Post-potentials (in Spanish),” in Latin-American Congress of Bio-Engineering, Havana, Cuba, May 2001. 2. Alberto Taboada Crispí, “Suitable Sudden Cardiac Death Predictor System,” in Proc. 9th Annual Conference on Student Research, UNB/Fredericton, Canada, February 2001. 3. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “A PC-based System for Ventricular Late Potential Analysis,” in Proc. CMBEC’2000, Halifax, Canada, October 2000.

Vita

4. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Data-base to Evaluate Algorithms for Ventricular Late Potential Detection (in Spanish),” in Proc. TECBIOMED ’99, ICID, Havana, Cuba, November 1999. 5. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Detection of Ventricular Late Potentials in a Limited Signal Segment (in Spanish),” in Proc. TECBIOMED ’99, ICID, Havana, Cuba, November 1999. 6. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Station to Detect Ventricular Late Potentials (in Spanish),” in Proc. 40th Anniversary Electrical Engineering Faculty, UCLV, Cuba, November 1999. 7. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Signal Processing in Ventricular Late Potential Detection (in Spanish),” in Proc. 1st Forum Informatics in Health, University Hospital “Arnaldo Milían Castro”, Santa Clara, Cuba, June 1999. 8. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Dennis F. Lovely, “Evaluation of the Alignment in the ECG Signal Coherent Averaging (in Spanish),” in Proc. 9th Symposium Electric Engineering, SIE ’99, UCLV, Cuba, February 1999. 9. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Rubén Orozco Morales, “Experimental System for Evaluation of Alignment Algorithms Used to Detect Late Potentials,” in Proc. World Congress on Medical Physics and Biomedical Engineering, Nice, France, September 1997. 10. Alberto Taboada Crispí, Juan V. Lorenzo Ginori, and Rubén Orozco Morales, “Experimental System to Detect and Analyse Ventricular Late Potentials (in Spanish),” in Proc. TECBIOMED ’96, ICID, Havana, Cuba, November 1996. 11. Alberto Taboada Crispí and Orlando Regalón, “Characterization of an Infusion Pump/Set System (in Spanish),” in Proc. 2nd Provincial Bioengineering Meeting, University Hospital “Arnaldo Milían Castro”, Santa Clara, Cuba, June 1995. 12. Alberto Taboada Crispí, “Biological Feedback to Relax (in Spanish),” in Proc. 2nd Provincial Bioengineering Meeting, University Hospital “Arnaldo Milían Castro”, Santa Clara, Cuba, June 1995. 13. Orlando Regalón and Alberto Taboada Crispí, “Infusion Pump/Set System (in Spanish),” in Proc. 7th Symposium Electric Engineering, SIE ’95, UCLV, Cuba, June 1995.

Vita

14. Alberto Taboada Crispí, “Automatic Twilight Switch (in Spanish),” in Proc. 6th Symposium Electric Engineering, SIE ’93, UCLV, Cuba, May 1993. 15. Emilio González and Alberto Taboada Crispí, “Integrative Courses in Technical Teaching (in Spanish),” in Proc. 12th Scientific Methodological Conference, UCLV, Cuba, December 1991. 16. Alberto Taboada Crispí, “Information Measurement System (in Spanish),” in Proc. 2nd Scientific Technical Event on Metrology, State Normalization Centre (CEN), Santa Clara, Cuba, December 1990. 17. Alberto Taboada Crispí, “Arc Effective Duration Measurer (in Spanish),” in Proc. 3rd International Symposium on Welding, Research Centre on Welding (CIS), UCLV, December 1990. 18. Alberto Taboada Crispí, “Voltage and Current Conditioning for a Welding-Parameter Measurement System (in Spanish),” in Proc. 5th Symposium Electric Engineering, SIE ’93, UCLV, Cuba, November 1990. 19. Alberto Taboada Crispí, “Welding Signal Processing (in Spanish),” in Proc. 2nd International Symposium on Welding, Research Centre on Welding (CIS), UCLV, Cuba, December 1989. 20. Alberto Taboada Crispí, “Current loops for serial communication (in Spanish),” in Proc. 1st Meeting of the Electronics Front, UCLV, Cuba, May 1989. 21. Emilio González and Alberto Taboada Crispí, “Training Kit MAQUELEC (in Spanish),” in Proc. 1st Meeting of the Electronics Front, UCLV, Cuba, May 1989. 22. Alberto Taboada Crispí, “Communication Interface (in Spanish),” in Proc. 2nd Symposium of Electronics and Automation, UCLV, Cuba, May 1989.

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