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Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmonicity constraints on the recovered basis functions. This paper proposes a new additive synthesis-based approach which allows the use of linear-frequency spectrograms as well as imposing strict harmonic constraints, resulting in an improved model. Further, these additional constraints allow the addition of a source filter model to the factorisation framework, and an extended model which is capable of separating mixtures of pitched and percussive instruments simultaneously.
Fitzgerald, D., Cranitch, M., Coyle, E. (2008) Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation. Computational Intelligence and Neuroscience Volume 2008, Article ID 872425, doi:10.1155/2008/872425