A method for separation of overlapping partials based on similarity of temporal envelopes in multi-channel mixtures

In a situation where multiple sound sources are concurrently active, the signals of the individual sources often overlap in time and in frequency. This is particularly likely for voiced instruments where the frequencies of some of the partials of one single note coincide with the frequencies of some of the partials of another instrument playing a harmonically related note. A source separation algorithm suitable for musical applications must address the problem of overlapping partials. A method is proposed for the separation of overlapping narrow-band partials in multi-channel mixtures. The method is based on the observation that, for many instruments, all the partials of a single note have similar temporal envelopes. For narrow band partials these similarities can be exploited in order to estimate demixing matrices in the frequency domain. Effectively, one can recover estimates of the original partials from a multi-channel mixture where they overlap. The method is computationally efficient in that it works on highly downsampled narrow frequency bands. It performs well for closely spaced and colliding partials, and (to some extent) also for frequency modulations such as vibrato effects