Harmonic analysis and restoration of separation methods for periodic signal mixtures: Algebraic separation versus comb filtering

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. The insight obtained via this analysis leads to the development of harmonic restoration techniques that fill in the information missing at the harmonics shared by the components and also to the development of constraints on the carrier frequencies and bandwidths for narrowband, bandpass, and periodic AM–FM components for minimum information loss. The restored methods are then applied to mixtures of sines and AM–FM signals. Differences between this improved approach and a similar improvement of the comb filtering approach are also emphasized.