OUTLINE - Digital Systems and Media Computing Laboratory

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J. W. Leis: “Digital Signal Processing Using MATLAB for Students and ... S. K. Mitra: “Digital Signal Processing: A Computer Based Approach”, McGraw-.
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OUTLINE

"  !. ". #$%&'() $(* +. !,(-.(-%/0120): "!"#$%&' ()*+*,-%./% 0'µ%123 &%$ ($&45%3“, 3224,*$% !,0*$.% 5(,6/*-.7µ*0, 2003 "  J. W. Leis: “Digital Signal Processing Using MATLAB for Students and Researchers”, J. Wiley & Sons, 2011

A. N. Skodras Computer Science School of Science and Technology Hellenic Open University Patras, Greece ! +30 2610 367522 / 367532

" +30 2610 367528 / 361106

! [email protected] # dsmc.eap.gr HELLENIC OPEN UNIVERSITY © 2011

4INTRODUCTION 4SIGNALS & SYSTEMS 4DISCRETE FOURIER TRANSFORM (DFT) 4FAST FOURIER TRANSFORM (FFT) 4Z-TRANSFORMS

"  S. K. Mitra: “Digital Signal Processing: A Computer Based Approach”, McGrawHill, 1998 "  P.A. Lynn and W. Fuerst: “Introductory Digital Signal Processing With Computer Applications", J. Wiley & Sons, 1989 " D.J DeFatta, J.G. Lucas and W.S. Hodgkiss: "Digital Signal Processing: A System Design Approach", J. Wiley & Sons, 1988 "  R.D. Strum and D.E. Kirk: "First Principals of Discrete Systems and Digital Signal Processing", Addison-Wesley Publishing Company, 1988

4FIR FILTER DESIGN

" E.C. Ifeachor and B.W. Jervis: “Digital Signal Processing: A practical approach”, Addison-Wesley Publishers, 1993

4IIR FILTER DESIGN

" J.G. Proakis and D.G. Manolakis: “Digital Signal Processing: Principles, Algorithms and Applications”, Prentice Hall, 1996 HELLENIC OPEN UNIVERSITY © 2011

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Why Signal Processing?

http://dsmc.eap.gr/downloads/dsp/dsp-0-1.pdf http://dsmc.eap.gr/downloads/dsp/dsp-0-2.pdf http://dsmc.eap.gr/downloads/dsp/dsp-0-9.pdf http://dsmc.eap.gr/downloads/dsp/dsp-1-1.pdf http://dsmc.eap.gr/downloads/dsp/dsp-1-2.pdf http://dsmc.eap.gr/downloads/dsp/dsp-1-9.pdf http://dsmc.eap.gr/downloads/dsp/dsp-2-1.pdf http://dsmc.eap.gr/downloads/dsp/dsp-2-2.pdf http://dsmc.eap.gr/downloads/dsp/dsp-2-9.pdf

Because: 4 Why signal processing

1.  Many times signals are “hidden”

4 Why digital signal processing (DSP)

2.  Signals can be “seen” more clearly in a different way or from a different perspective

4 What DSP is?

3.  …

4 Where DSP is applied? 4 Which are the key DSP operations?

http://dsmc.eap.gr/downloads/dsp/dsp-book.pdf

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Example

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ILLUSTRATIVE EXAMPLE OF A NOISY SIGNAL

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Time domain representation obscures the fact that the signal is actually not a single sinusoid, but the sum of three sinusoids, that is X(t)=cos(2! " 5t) + 100 " cos (2! " 10t) + 0.5 " cos (2! " 20t) The sinusoid whose amplitude is 100 dominates the picture. HELLENIC OPEN UNIVERSITY © 2011

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• Removing mains-frequency interference from an ECG

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DSP example: Adaptive Filtering of Ocular Artefacts from the Human EEG

Adaptive ocular artefact removal method: (a) possible electrode positions for EOG (ocular movement) and EEG measurements; (b) adaptive ocular artefact filter. HELLENIC OPEN UNIVERSITY © 2011

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DSP example: Foetal Monitoring – Canceling of Maternal ECG

The problem of ocular artefacts in electroencephalography: (a) measured EOG, (b) corresponding contaminated EEG signal and (c) EEG signal corrected for artefact. HELLENIC OPEN UNIVERSITY © 2011

Adaptive canceling of maternal ECG in foetal ECG (after Widrow et al., 1975a): (a) cardiac electric field vectors and foetus; (c) adaptive; (d) idealized mother’s ECG (chest leads); (e) idealized contaminated foetal ECG (abdominal lead); (f) output of noise canceller showing reduced mother’s ECG. HELLENIC OPEN UNIVERSITY © 2011

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DSP example: Adaptive Telephone Echo Cancellation

Source: http://www.usq.edu.au/users/leis/courses/ELE3107/LectureSlides/module1.pdf HELLENIC OPEN UNIVERSITY © 2011

The compact disc digital audio system

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The Stock Market Example

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BASIC DIGITAL SIGNAL PROCESSING ALGORITHMS ANALOG SIGNAL PROCESSING

FILTERS Example:

- Temperature variations - Component aging - Power-supply variations - Component accuracy have to be considered. The resulting circuit: - Has low noise immunity - Requires adjustments - Is difficult to modify

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DIGITAL SIGNAL PROCESSING

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Digital Signal Processing System

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Why Digital Signal Processing? Because: Digital computers are inexpensive

Digital Signal Processing is related to many other areas of science, engineering and mathematics:

Advantages: •  Greater flexibility (adaptive filters easily implemented) •  Self-test can be built-in •  Perfect reproducibility •  Guaranteed accuracy •  High noise immunity and power supply rejection •  No drift •  Superior performance •  Time-sharing possibility

Summary of key DSP operations (1) Convolution: Given two finite length sequences, x(n) and h(n), of lengths N1 and N2 ,respectively, their linear convolution is

where M=N1+N2-1

Disadvantages: •  Speed HELLENIC OPEN UNIVERSITY © 2011

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(2) Correlation: (a) Given two N- length sequences, x(k) and y(k), with zero means

an estimate of their cross-correlation is given by

where

is an estimate of the cross-covariance and defined as

(b) An estimate of the autocorrelation, ρxx(n), of an N-length sequence, x(k), with zero mean is given by

where rxx(n) is an estimate of the autocovariance and defined as

(3) Filtering: The equation for finite impulse response (FIR) filtering is

where x(k) and y(k) are the input and output of the filter, respectively, and h(k), k=0,1,…,N-1, are the filter coefficients. (4) Discrete transform:

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Correlation examples Autocorrelations of (a) a periodic signal, (b) noise and (c) periodic signal plus noise. Note that in (c) the periodic nature of the signal buried in noise is still evident, illustrating why autocorrelation is used in detecting hidden periodicity.

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Cross-correlation of a random signal, x(t), and a delayed noisy version of the same signal, y(t). The delay between the two signals is the time from the origin to the time where the peak occurred in their cross-correlation in (c ). HELLENIC OPEN UNIVERSITY © 2011