Robust Parametric Modeling of Speech in Additive White Gaussian Noise

Abdelaziz Trabelsi¹, Otmane Ait Mohamed¹, Yves Audet²

¹Department of Electrical and Computer Engineering, Concordia University, Montréal, Canada.
²Department of Electrical Engineering, école Polytechnique de Montréal, Montréal, Canada.

DOI: 10.4236/jsip.2015.62010                

Abstract

In estimating the linear prediction coefficients for an autoregressive spectral model, the concept of using the Yule-Walker equations is often invoked. In case of additive white Gaussian noise (AWGN), a typical parameter compensation method involves using a minimal set of Yule-Walker equation evaluations and removing a noise variance estimate from the principal diagonal of the autocorrelation matrix. Due to a potential over-subtraction of the noise variance, however, this method may not retain the symmetric Toeplitz structure of the autocorrelation matrix and thereby may not guarantee a positive-definite matrix estimate. As a result, a significant decrease in estimation performance may occur. To counteract this problem, a parametric modelling of speech contaminated by AWGN, assuming that the noise variance can be estimated, is herein presented. It is shown that by combining a suitable noise variance estimator with an efficient iterative scheme, a significant improvement in modelling performance can be achieved. The noise variance is estimated from the least squares analysis of an overdetermined set of p lower-order Yule-Walker equations. Simulation results indicate that the proposed method provides better parameter estimates in comparison to the standard Least Mean Squares (LMS) technique which uses a minimal set of evaluations for determining the spectral parameters.

Keywords

ARMA Model, Noise Variance, Overdetermined Parametric Evaluation, Singular Value Representation, LMS Technique, Yule-Walker Equations

Conflicts of Interest

The authors declare no conflicts of interest.

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