HARMONIC-ANALYSIS AND RESTORATION OF SEPARATION METHODS FOR PERIODIC SIGNAL MIXTURES - ALGEBRAIC SEPARATION VERSUS COMB FILTERING

The problem of separating a mixture of periodic signals into its const ituent components occurs in sound detection, biomedical signal process ing, and in communications. Existing approaches to solving it are eith er based on harmonic selection in the frequency domain or on linear co mb filtering in the time-domain. In this paper, the recently proposed matrix algebraic separation approach is analyzed in the frequency doma in. 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 narrowban d, bandpass, and periodic AM-FM components for minimum information los s. The restored methods are then applied to mixtures of sines and AM-F M signals. Differences between this improved approach and a similar im provement of the comb filtering approach are also emphasized. (C) 1998 Elsevier Science B,V. All rights reserved.