Separation of a Mixture of Independent Signals Using Time Delayed Correlations

The problem of separating n linearly superimposed uncorrelated signals and determing their mixing coefficents is reduced to an Eigenvalue problem which involves the simultaneous diagonalisation of two symmetric matrices whose elements are measureable time delayed correlation functions. The diagonalisation matrix can be determined from a cost function whose number of minima is equal the number of degenerate solutions. Our approach offers the possibility to separate also nonlinear mixtures of signals. PACS numbers:02.50.+s, 05.40.+j, 06.50.-x, 87.71.-p Typeset using REVT E X The problem of source separation appears in many contexts. The most simple situation occurs for two speakers. If the mixture of their voices reaches two microphones one wants to separate both sources such that each detector registers only one voice [1]. Typical examples involving many sources and many receivers are the separation of radio or radar signals by an array of antennas [2], the separation of odors in a mi..