Separation of harmonic instruments with overlapping partials in multi-channel mixtures

When instruments play together, different partials often overlap in time and frequency. This is particularly likely for harmonic instruments. We present a new method for the separation of overlapping partials in multi-channel mixtures. The method is based on the observation that when a harmonic instrument plays a note, all the partials have similar shapes, i.e. common onset, offset, amplitude and frequency modulation. For narrowband partials, we devise a method to estimate a demixing matrix that can recover the original source partials from the multi-channel mixture where they overlap. The method is computationally efficient in that it works on highly downsampled narrow frequency bands and it performs equally well for closely spaced partials as for crossing partials, e.g., due to frequency modulations such as vibrato effects. It is able to separate partials in mixtures with a high number of overlapping partials, such as two instruments playing notes where the fundamental frequencies are in fifth (3:2) or octave (2:1) relation.