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
designed input-to-state filter in connection with interpreting the
estimated state-covariances via standard tools from interpolation
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.