Multichannel relative-entropy spectrum analysis

A new relative-entropy method is presented for estimating the power spectral density matrix for multichannel data, given correlation values for linear combinations of the channels, and given an initial estimate of the spectral density matrix. A derivation of the method from the relative-entropy-principle is given. The basic approach is similar in spirit to the multisignal relative-entropy spectrum analysis of Johnson and shore, but the results differ significantly because the present method does not arbitrarily require the final distributions of the various channels to be independent. For the special case of separately estimating the spectra of a signal and noise, given the correlations of their sum, multichannel relative-entropy spectrum analysis turns into a two-stage procedure. First, a smooth power spectrum model is fitted to the correlations of the signal plus noise. Then, final estimates of the spectra and cross spectra are obtained through linear filtering. For the special case where p uniformly spaced correlations are known, and where the initial estimate of the signal-plus-noise spectrum is all-pole with order p or less, this method fits a standard maximum-entropy autoregressive spectrum to the noisy correlations, then linearly filters to calculate the signal and noise spectra and cross spectra. Consideration is given to the case where only an initial estimate of the noise power spectrum is available. An illustrative example is given.