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The Unified Framework

In a sense, all approaches can be thought of as an attempt to project each individual source onto a subspace which is orthogonal to the others. While being suitable for tonal signals, the Fourier transform can only concentrate sinusoidal energy into the corresponding coefficients but do nothing to help separate contributions from different sources. The problem is aggravated by the time-frequency resolution conflict which raises the possibility of more than one sources being overlapped in the time-frequency space. Wavelet transform has been used to make up for the inadequacy of the Fourier transform. Wavelet transform resolves the conflicting need in resolution at low and high frequencies. It is a closer approximation to what the ear does; resolving less well in the high frequency region. having constant Q-ratio, it still does not know one source from the other. ICA is an attempt to see through the physical meaning and derive the subspaces where the mixture projection is most ``independent'' and hence, according to the model, should be the sources. However, it is data driven and non-parametric, making it data sensitive and unsuitable for modification.



Pamornpol Jinachitra
Tue Jun 17 16:27:28 PDT 2003