Spectral Estimation via Selective Harmonic Amplification

Tryphon T. Georgiou
University of Minnesota

The state covariance of an input-to-state filter imposes analytic interpolation constraints on the spectrum of the input.

This basic observation makes analytic interpolation theory especially relevant in the context of spectral estimation. In particular, a suitably designed input-to-state filter in connection with interpreting the estimated state-covariances via standard tools from interpolation theory, is capable of resolution significantly higher than pre-existing state-of-the-art estimation algorithms.

In the talk we will focus on a decomposition theorem for state covariance matrices and its application to high resolution subspace methods, estimation of spectral envelopes, and absorption spectra. We will also review recent progress in analytic interpolation theory with degree constraint.