The state-covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter, and also imposes a generalized interpolation constraint on the power spectrum of the input process. This algebraic property and the relationship between state-covariance and the power spectrum of the input allow the use of matrix pencils and analytic interpolation theory for spectral analysis. Several algorithms for spectral estimation will be developed with resolution higher than state of the art.
Bibliographical noteFunding Information:
Manuscript received April 23, 1999; revised November 30, 1999, February 28, 2000, and March 22, 2000. Recommended by Associate Editor T. Parisini. This work was supported in part by the National Science Foundation and in part by AFOSR.