Estimation of LPC Parameters of Speech Signals in Noisy Environment Akshya K. Swain
Waleed Abdulla
Department of Electrical and Computer Engineering, University of Auckland, Private Bag-92019 , Auckland, New Zealand email:
[email protected],
[email protected] Abstract— The performance of LPC based algorithm deteriorates significantly in the presence of background noise. The present study proposes a new approach based on orthogonal least squares (OLS) algorithm with structure selection to obtain unbiased LPC parameters from noisy speech samples. Instead of fitting a fixed order model to all segments of speech, the algorithm selects the best possible model order for a given speech segment using an error reduction ratio (ERR) test. A noise model is appended to the conventional LPC model to make the LPC parameters unbiased. The proposed algorithm gives superior performance compared to the commonly used LPC based algorithm under high levels of noise.
I. I NTRODUCTION Linear prediction based speech analysis has received considerable attention in the past four decades. In linear prediction, the speech waveform is represented by a set of parameters of an all-pole model, called the linear predictive coefficients (LPC), which are closely related to speech production transfer function. The LPC analysis essentially attempts to find an optimal fit to the envelope of the speech spectrum from a given sequence of speech samples. The LPC feature computed by autocorrelation or covariance method (Makhoul,1975) minimizes the sum of squares of the prediction residuals and therefore resembles a least squares fit. The performance of LPC technique, which is equivalent to auto regressive (AR) modeling of the speech signal, however degrades significantly in the presence of background noise. The additive noise changes speech signal process from AR to an auto regressive moving average (ARMA) process. The least squares estimates of the LPC parameters from a noise corrupted sequence using an all-pole speech model therefore become biased ; the bias being proportional to the inverse of the signal-to-noise ratio (Soderstrom and Stoica,1989). Several techniques based around robust statistic, instrumental variables and higher order Yule-Walker equations have been suggested in the past to obtain improved estimates of linear predictive coefficients from noisy speech samples (Lee,1988; Ramachandran et al,1995; Gong, 1995,Hernando and Nadeu,1997, Shimamura, 2001) . The present study proposes an alternative approach to estimate the LPC parameters using orthogonal least squares algorithm with structure selection (Billings et al et al,1989; Swain and Billings,1998). An error reduction ratio (ERR) test
, which is a byproduct of the OLS algorithm, is used to find the best possible order for a given speech segment and to include only those terms which are significant into the model. Estimation of the model coefficients become straightforward once the terms to be included are known. The model terms are quantified according to the contribution they make to the variance of speech segment. The best model is selected as the model which explains the total signal variance and for which the number of terms is a minimum. This implies that the model terms are selected according to their significance to the signal variance. The biasing effects of noise on signal related parameters (LPC parameters) can be reduced significantly by appending a noise model where the estimation of signal and noise model parameters are decoupled. The performance of the algorithm has been demonstrated with examples of spoken words with high levels of noise and has been found to be superior compared to LPC based algorithms. The organization of the paper is as follows. Section-II gives the details of the problem formulation when the speech signal is corrupted by noise. A brief review of the orthogonal least squares algorithm and some model validation methods are presented in section-III . The effectiveness of the proposed algorithm is illustrated in section-IV with conclusions in section-V. II. P ROBLEM F ORMULATION The block diagram of a LPC based speech production model in noise is shown in Fig.1 where the speech signal is modeled as the output of an all pole filter which is excited by a sequence of pseudo periodic pulses for voiced speech or pseudo random noise for unvoiced speech. Thus within a certain window length of speech the output speech sequence is modeled (without noise and preemphasis filter) as
! #"$ % '&(&(&) *)+ , *- /.10325467/ 8 9;:A@ < =?> CD E B )G H , JIK L.'MON H (1) F where p is the order of the LPC model,w(n) is the widow N P QN/ 5 SRPTU is the windowed version of the function,
+ D B , S. D ! F F .3MON (" / /. H P H /R TU 5
+
All Pole Filter
Preemphasis
Fig. 1. Block diagram of Linear Prediction Based Speech Production Model
H P H LR TU 5
input excitation u(n), G is the gain of the filter, v(n) is the is the windowed speech additive noise, signal, ’s are the LPC coefficients characterizing the filter and is the residual error. Since it is customary to pass the speech signal through a preemphasis filter of the form "! to boost the signal spectrum by 6dB/octave, the model of eqn.(1) with preemphasis filter becomes %$ # # # "! (2) &(' *)
" /)
4 7/
4 H 7 #"$ #& &(& 4 7 5 .J032 4 7/ % 032 4 7 ' B" 8 9;:
