Blind separation of convolutive mixtures by decorrelation

Authors:
Tiemin Mei;Fuliang Yin
Affiliations:
Department of Electronic Engineering, School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116023, PR China;Department of Electronic Engineering, School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116023, PR China
Venue:
Signal Processing
Year:
2004

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Abstract

This paper mainly deals with the necessity and the sufficiency of decorrelation criterion for the separation of convolutive mixtures. Although this problem has been studied in frequency domain, it is still necessary to reformulate this problem in time domain. In this paper, it is proved that decorrelation is a sufficient condition for the separation of convolutive mixtures in time domain, and some new results are presented in this paper. First, separation filters do not always approximate the mixing filters (the responses of the channels in which the sources are transformed and mixed) in time domain, they much frequently approximate the mixing filters in the nonzero spectral band of sources in frequency domain, so the separation filters are usually not unique. Second, imposing some constraints on the equivalent mixing filters, the blind separation of convolutely mixed signals is proved to be equivalent to the optimum filtering problem on the basis of the backward separation system. Third, we propose the Double-LMS and -RLS algorithms for the separation of two convolutely mixed sources by means of the standard LMS and RLS algorithms. These algorithms are naturally generalized to multi-source separation problem, that is, the Multi-LMS and -RLS algorithms. The numerical experiments are presented to illustrate the validity of our algorithms.