Harmonic Analysis and Restoration of Separation Methods for Periodic Signal Mixtures: Algebraic Separation Vs. Comb Filtering
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Abstract:
The problem of separating a mixture of periodic signals into its constituent components occurs in sound detection, biomedical signal processing, and in communications. Existing approaches to solving it are either based on harmonic selection in the frequency domain or on linear comb filtering in the time--domain. In this paper, the recently proposed matrix algebraic separation approach is analyzed in the frequency domain, This harmonic analysis leads to an improvement of the algebraic method by restoring some of the missing information in the harmonics shared by the components. The restored method is then applied to separating the components of mixtures of three types of periodic signals: sines, AM-FM signals, and synthetic vowels. Differences between this improved approach and a similar improvement of the comb filtering approach are also emphasized.
