Minimum cross-entropy spectral analysis of multiple signals

This paper presents a new information-theoretic method for simultaneously estimating a number of power spectra when a prior estimate of each is available and new information is obtained in the form of values of the autocorrelation function of their sum. One application of this method is the separate estimation of the spectra of a signal and additive noise, based on autocorrelations of the signal plus noise. A derivation of the method from the principle of minimum cross entropy is given, and the method is compared to minimum cross-entropy spectral analysis, of which it is a generalization. Some basic mathematical properties are discussed. Three numerical examples are included, two based oil synthetic spectra, and one based on actual speech data.