Recently, a new tool known as Nonnegative Matrix Factorization (NMF) has presented itself as a formidable and useful tool for providing a parts based representation of matrix data. It has been applied with success in audio signal processing for topics such as blind source separation (BSS), music transcription and for representing musical and/or speech mixtures as additively occurring nonnegative representations of audio components. This thesis presents research and a proposed algorithm that addresses the problem of under-determined multi-channel frequency domain BSS, and investigates spatial covariance matrix (SCM) based NMF and single channel CNMF algorithms as applied to complex (as opposed to nonnegative) STFT coefficients. The research also investigates K-means clustering applied to interchannel frequency dependent phase differences in order to achieve source separation using SCM NMF based techniques.

Keywords: Nonnegative Matrix Factorization; Complex Matrix Factorization; Spatial Covariance Matrices; Underdetermined multi-channel source separation; Blind Source Separation; multi-channel STFT