Spectral Analysis from Multi-Rate Observations: Itakura-Saito based Approximation of Power Spectra and Capon-like Spectral Envelopes

We develop a framework for spectral analysis in the context of multi-rate sampling by a collection of sensors. Correlation of the time-domain samples gives rise to moment constraints for the power spectrum. We use a homotopy based technique to identify a power spectrum which is closest to a given "prior" in the Itakura-Saito distortion sense and is also consistent with the given moment statistics. It turns out that this power spectrum is the harmonic mean of the prior and a suitable "all-pole" spectral density. We then proceed to adapt the framework so as to obtain Capon-like spectral envelopes based on the same autocorrelation data