Statistical properties of signals approximated by orthogonal polynomials and Schur parametrization

Abstract

In the paper, we investigate reconstruction of statistical properties of signals approximated in various orthogonal bases. The approximation of signals is performed in various polynomial bases and by Schur parametrization algorithm. To compare quality of remodeled signals in different bases, we use mean square error criterion for power spectral density. The correlation function, and the derived from it power spectral density, is sufficient to describe signal statistical properties. The numerical experiments were performed using benchmark signals. The tests were executed for different polynomial degrees and different orders of Schur innovation filtering. Our purpose was to find which patrametrization method requires less parameters.