Analysis of the stability of time-domain source separation algorithms for convolutively mixed signals

In this paper, we investigate the self-adaptive source separation problem for convolutively mixed signals. The proposed approach uses a recurrent structure adapted by a generic rule involving arbitrary separating functions. We first analyze the stability of this class of algorithms. We then apply these results to some classical rules for instantaneous and convolutive mixtures that were proposed in the literature but only partly analyzed. This provides a better understanding of the conditions of operation of these rules. Eventually, we define and analyze a normalized version of the proposed type of algorithms, which yields several attractive features.