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Computational Intelligence and Neuroscience
Volume 2008 (2008), Article ID 872425, 15 pages
Research Article

Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation

1Department of Electronic Engineering, Cork Institute of Technology, Cork, Ireland
2School of Electrical Engineering Systems, Dublin Institute of Technology, Kevin Street, Dublin, Ireland

Received 18 December 2007; Revised 3 March 2008; Accepted 17 April 2008

Academic Editor: Morten Morup

Copyright © 2008 Derry FitzGerald et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.