Blind identification of slightly delayed mixtures

We are interested in the separation of N propagating source signals recorded simultaneously by a set of receivers. To solve this “cocktail-party problem”, we propose to collect a set of spatially close microphones. On each sensor, signals are received with the same attenuation but with different time delays. The linear memoryless conventional model for source separation is then no longer suitable. However, when time delays are small in comparison with the coherence time of each source, we show that this problem can be simplified building up a particular set of instantaneous mixtures involving derivatives of sources with respect to time. Then, sources can be extracted using second-order methods. The limitations of the method are exposed: we explain what a small delay is and we show that the number of sources cannot exceed 3. The validity of the proposed approach is confirmed by computer simulations. Finally, we apply our method to an experiment where two source signals are extracted from their mixtures observed with two omnidirectional microphones in a normal room