Self-adaptive separation of convolutively mixed signals with a recursive structure. Part II: Theoretical extensions and application to synthetic and real signals

This paper deals with the separation of two convolutively mixed signals. Th e proposed approach uses a recurrent structure adapted by generic rules inv olving arbitrary separating functions. While the basic versions of this app roach were defined and analyzed in our companion paper (Charkani and Devill e, 1999), two extensions are considered here. The first one is intended for possibly colored signals. In addition, the second one may be used even whe n the probability density functions of the sources are unknown. We first an alyze the convergence properties of these extended approaches at the separa ting state, i.e. we derive their equilibrium and stability conditions and t heir asymptotic error variance. We then determine the separating functions which minimize this error variance. We also report experimental results obt ained in various conditions, ranging from synthetic data to mixtures of spe ech signals measured in real situations. These results confirm the validity of the proposed approaches and show that they significantly outperform cla ssical source separation methods in the considered conditions. (C) 1999 Els evier Science B.V. All rights reserved.