Blind source separation of audio streams using wavelets

In this thesis, Blind Source Separation is studied in the context of both instantaneous and convolutive mixtures of musical sources. In order to appreciate how the application of BSS techniques to music may differ from application to speech samples, the statistical and spectral characteristics of commercial musical recordings are determined. Furthermore, the extent to which certain assumptions underlying many BSS (or, more generally, ICA) techniques are valid is investigated. The use of short-time Fourier Transform techniques in BSS is discussed, and the use of wavelet and wavelet-packet techniques to perform BSS is investigated. The most efficient wavelets to use for the decomposition of musical sources are determined, and measures of the sparsity of transformed sample data are compared for different transform techniques. A number of strategies for reducing the computational complexity of the application of BSS techniques are developed (principally around the use of wavelet transforms). Summaries of the most popular BSS techniques (for both instantaneous and convolutive mixtures) are provided, and metrics frequently used to evaluate both signal separation and reconstruction performance are listed. To support the work of this thesis, a large library of Matlab routines has been developed. Throughout the work, clear examples are provided to support the theoretical discussion. This thesis concludes with a summary of the investigations performed, and an outline of future research directions suggested by the work contained herein

Statistical, spectral and stochastic characteristics of music

The goal of this paper is to explore some of the principal spectral and statistical characteristics of music that are relevant to the problem of Blind Source Separation (BSS). Some BSS algorithms require some a priori knowledge of statistical characteristics of the mixtures under examination, if only to more accurately establish initial estimates. Furthermore, theoretical investigations depend upon the assumption of Wide-Sense Stationarity - the extent to which this assumption holds is investigated

Wavelet-based transforms as a means of signal separation

The goal of this paper is to facilitate the use of waveletbased transforms in BSS (and, more generally, ICA) algorithms. We investigate the performance of transforms such as the ContinuousWavelet Transform, Discrete Wavelet Transform and Discrete Wavelet Packet Transform relative to the commonly-used Short-Time Fourier Transform in terms of the efficiency of signal-power representation and the minimisation of cross-channel effects in two-channel mixtures