Comparison and a Theoretical Link between Time-domain and Frequency-domain Blind Source Separation

The problem of separating convolutive mixtures of unknown time series arises in several application domains, a prominent example being the so-called cocktail party problem, where we want to recover the speech signals of multiple speakers who are simultaneously talking in a room. The room may be very reverberant due to reflections on the walls, i.e., the original source signals sq(n), q = 1, . . . , P of our separation problem are filtered by a multiple input and multiple output (MIMO) system before they are picked up by the sensors xp, p = 1, . . . , P . An M -tap mixing system is thus described by