On Signal Separation by Second Order Statistics
Abstract:
The problem of separating two or more uncorrelated signals from equally many observed mixtures is considered in this thesis. The observed signals are modeled as a sum of original signals filtered through linear filters. Various kinds of mixing filters are considered: Finite Impulse Response (FIR) and Auto Regressive Moving Average (ARMA), causal and non-causal, one and two-dimensional. A separation structure is used in order to extract the original signals from the observed signals. Separation structures are presented both for a Two Input Two Output (TITO) scenario and for a Multi Input Multi Output (MIMO) scenario. Two types of algorithms, both based on second order statistics, are presented in order to estimate the coefficients of the filters in the separation structure. The first type of algorithms are based on minimizing a criterion which is the sum over different lags of squared cross-correlations of the separation structure output. The second type of algorithm is based on a system identification approach, using the Recursive Prediction Error Method (RPEM). The Cram'er Rao Lower Bound is derived for the signal separation problem. This
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