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Approche temps-fréquence pour la séparation aveugle de sources non-stationnaires

Abstract : This work concerns Blind Source Separation (BSS). BSS consists in estimating n unknown signals (the sources) from the sole observation of m mixtures of them (the observations).
We first study identifiability of the sources for the problem of linear instantaneous mixtures separation, in the (over-)determined case (m ≥ n).
Several models of the sources are studied. In particular, it is showed that if the sources have time and/or frequency diversity, their mutual independence at order 2 is sufficient to guarantee identifiability.
Then we describe a few BSS methods designed from the hypotheses of the studied identifiable models. These methods are based on the joint-diagonalization of several matrices. In particular we study a method designed for non-stationary sources, which relies on matrices extracted from the Spatial Wigner-Ville Spectrum (SWVS) of the observations at particular time-frequency locations (and after spatial whitening). We propose a theoretical approach in a stochastic context which justifies in practice the approximation of the SWVS by Cohen's class Spatial Time-Frequency Representations. The performance of the method strongly relies on the selection of time-frequency points and we propose a robust selection criterion based on single auto-terms from the sources. A statistical study of the performance of the methods is carried out on synthetic TVARMA non-stationary sources. Some original evaluation criteria are proposed.
Finally, we show how the studied methods for the separation of linear instantaneous mixtures can be extended to the case of convolutive mixtures with Finite Impulse Response. Some results on synthetic mixtures of audio signals are presented.
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Contributor : Cédric Févotte <>
Submitted on : Wednesday, February 2, 2005 - 8:06:52 PM
Last modification on : Thursday, January 7, 2021 - 8:18:13 PM
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  • HAL Id : tel-00008340, version 1

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Cédric Févotte. Approche temps-fréquence pour la séparation aveugle de sources non-stationnaires. domain_stic.inge. Ecole Centrale de Nantes (ECN); Université de Nantes, 2003. Français. ⟨tel-00008340⟩

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