Blind source seperation is based on PCA and ICA.

The principal component analysis (PCA) and independent component analysis (ICA) are methods to devide a mixture of sounds into uncorrelated or indendent components.

The PCA is based on the singular value decomposition (SVD) of a matrix or on the eigenvalue and eigenvector determination of a centered covarince or correlation matrix. 

PCA is applied in the method Spatial Transfrom of sound fields (STSF) to receive uncorrelated components from a mixture. The components are assumed to be coherent and projected by the method acoustic holography.

The method PCA was applied to simultaneous measurements of vibrations on the structure and sound in the far field. The components from the PCA are seperated into near field and far field components using the reaction of the far field microphone.  

The Doppler effect of moving sources in the far field was compensated either by correcting the transformation kernel from time to frequency domain or by re-sampling.

A better seperation of independent sources is possible, if ICA is applied. ICA in theory is based on the Kulback-Leibler divergency related to a Gaussian distribution to maximize a non-Gausianity. Approximations to this feature that are more stable and faster to optimize are used in the FastICA algorithms.

The FastICA code was applied to short pices of music and the notes were separated by this algorithm.