Blind source extraction using generalized autocorrelations

This letter addresses blind (semiblind) source extraction (BSE) problem when a desired source signal has temporal structures, such as linear or nonlinear autocorrelations. Using the temporal characteristics of sources, we develop objective functions based on the generalized autocorrelations of primary sources. Maximizing the objective functions, we propose simple fixed-point source extraction algorithms. We give the stability analysis and prove convergence properties of the algorithms as the generalized autocorrelation function is linear or nonlinear. Especially, as the generalized autocorrelation function is linear, the algorithm has interesting character of "one-iteration" convergence under some conditions. Computer simulations and real-data application experiments show that the algorithms are appealing BSE methods for temporal signals of interest by capturing the linear or nonlinear autocorrelations of the desired sources.