Adaptive blind separation of convolutive mixtures

The convolutive mixture separation problem is addressed. As soon as there are more sensors than sources, it can be solved using almost only the second order statistics of the observed signal, through a three-step method: first a linear prediction leads to the extraction of a multidimensional normalized innovation process of the observed signal, second the scalar innovation processes of the source signals are obtained thanks to an instantaneous mixture separation and third the contributions of each source in the mixture are recovered by filtering the innovation processes by the inverse of the prediction filter. A decomposed and normalized lattice synthesis filter is introduced. It solves the problem of singularity, and as it is stable for any choice of its parameters, this filter can be adaptively computed. Simulation results confirm this property.