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A shifted non-negative matrix factorisation algorithm is derived, which offers advantages over previous matrix factorisation techniques for the purposes of single channel source separation. It represents a sound source as translations of a single frequency basis function. These translations approximately correspond to notes played by an instrument. Results are presented for a set of synthetic data, and on a single channel recording of piano and clarinet. Though the system is aimed at musical recordings, the techniques can be applied to any data which contains shifted versions of an underlying factor, and so the algorithm could possibly be used in other applications such as image processing.
Fitzgerald, D., Cranitch, M., Coyle, E.: Shifted non-negative matrix factorisation for sound source separation. Proceedings of the Irish Signals and Systems Conference, Dublin, Ireland, 2005.