J. Le Roux

A fixed point computation of partial correlation coefficients

This paper introduces a new computational algorithm for the partial correlation coefficients of a linear system given the covariance of its output when excited by a white input noise. Although derived from Levinsons well-known procedure, the proposed algorithm does not make use of the usual parameters in the linear prediction recursion. It may be implemented using fixed point arithmetics. Application to speech waves is emphasized.

2-D Bauer factorization

The extension to the 2-D case of the Bauer formulation of the spectral factorization is given. The relation to the 2-D generalization of the Levinson algorithm by Marzetta leads to a proof of the convergence of the method. The problems of the practical implementation are discussed.

An iterative procedure for moving average models estimation

Using the formulation of Levinsons algorithm in terms of cross correlation estimates as presented by RISSANEN, it is shown that, in the case of a finite length autocorrelation serie R(z) (i.e. moving average models), this procedure generates a serie that converges towards a causal impulse response E(z) . This response has a finite length and its autocorrelation E(z)\cdotE(z^{-1}) is proportionnal to R(z) . Moreover it is shown that E(z) has all its roots inside or on the unit cercle (minimal phase response). The proof uses mainly the properties of the PARCOR coefficients.

Autoregressive models for noisy speech signals

Linear prediction is a well extended technique for transmission, synthesis and recognition. However when the signal is corrupted by noise, the estimation of the auto-regressive model is known to be biaised. This paper is devoted to methods allowing a reduction of this bias. We will consider first a global method, in which the Yule Walker equations are modified to take into account the variance of an additive white noise. The problem becomes non-linear and is solved recursively. In a second approach, we will examine a time - recursive method based on Kalman filtering.

Some properties and algorithms for fourth order spectral analysis of complex signals

In this paper, we give two algorithms for linear system blind identification based on the fourth order spectrum (or trispectrum). The first algorithm uses only N of the N/sup 3/ data of the fourth order spectrum. The second algorithm uses all the information contained in the fourth order spectra, but gives an optimal solution. This solution needs a previous phase unwrapping step; we give different solutions to unwrap the trispectrum phase. Finally, we establish the link between the well-known kurtosis maximization method and the optimal solution presented here; they are equivalent in first approximation. It means that we give an analytic solution to the blind identification problem which is nearly equivalent to the kurtosis maximization solution.Some algorithms for linear system identification based on fourth order spectra are given. They extend algorithms developed in the case of third order statistics. We also give a method for phase unwrapping for fourth order spectra and we establish a link between algorithms based on kurtosis maximization and identification method in the frequency domain.

System frequency response phase estimation based on skewness or kurtosis maximization

Higher order statistics are efficient for estimating the characteristics of linear systems frequency response, especially in terms of phases. Interesting methods are those based on kurtosis maximization. These methods have been developed essentially in the time domain. We give their transcription in terms of frequency response phases. These methods have been developed when the higher order spectrum is accurately estimated. Here we show through simulations and some partial theoretical justifications that they are also useful when the higher order spectrum estimate is not accurate.

Factorizability of complex signals higher (even) order spectra: a necessary and sufficient condition

This paper presents a necessary and sufficient condition for the factorizability of higher order spectra of complex signals. Such a factorizability condition can be used to test if a complex signal can model the output of a linear and time invariant system driven by a stationary non-Gaussian white input. The condition developed here is based on the symmetries of higher order spectra and on an extension of a formula proposed by Marron et al. (1990) to unwrap third order spectrum phases. It is an identity between the products of six higher order spectra values (which reduces to four values if only phases are considered). Our factorizability test requires no phase unwrapping, unlike existing methods developed in the cepstral domain. Moreover its extension to the N-th order case is direct. Simulations illustrate the deviation to this factorizability condition in a factorizable case (linear system) and a non-factorizable case (non-linear system).

Iterative and non iterative techniques for the design of recursive digital filters

Two algorithms are presented for designing recursive filters to give a desired spectral density characteristic. The first one is non iterative and fits correlation of the desired spectrum for getting pole-coefficients, then decomposes the reciprocal of MA-spectral density for calculating zero-coefficients. Both coefficients are calculated efficiently through the solution of two systems of equations using generalized Levinson algorithm. As this algorithm gives a suboptimal solution we propose the second algorithm which uses a Steiglitz type iterative solution for minimizing a square error criterion in the frequency domain. The steepest descent gradient method is used for getting coefficients of filters. From the point of view of implementation on a machine, the effect of coefficient quantization is considered.

PHONEMIC RECOGNITION BY LINEAR PREDICTION: EXPERIENCES AT ENST

The introduction of identification methods, stemming from System Theory and in particular the Linear Prediction has recently given rise to the development of new methodologies in signal analysis, ans especially in speech. The idea underlying these methods considers the vocal system as a filter belonging to a certain family parametric. According to this approach, the analysis of speech signals within this established mathematical framework enables the identification of the characteristic parameters of the signal. During a short period, the speech signal represented by the numerical value of these parameters. The inversion of the model permits checking the correctness of the hypotheses made, by producing a synthetic signal, the quality of which measures the validity of the model. For the past ten years, large advances have been made in the techniques of speech modelling, due to the ease of designing algorithmes on a computer.