The Circulant Rational Covariance Extension Problem for a Skew Periodic Stochastic Process

Abstract: The Rational Covariance Extension Problem is a problemin applied mathematics where one tries to find a rational spectral density thatmatches a finite covariance sequence. Applications of this can be used in areaslike speech- and image-processing. This problem has been studied intensivelyover the last decades and recently a related problem, the Circulant RationalCovariance Extension Problem, was solved. This version of the problem dealswith periodic stochastic sequences, and was shown to be a natural way toapproximate the solution to the original problem. Here we look at the specialcase when the process in question is skew-periodic, and show that also in thiscase a unique solution to the problem exists. Moreover we develop numerical solversfor both the periodic and the skew-periodic problem, and use these algorithms toapproximate the spectrum from a speech signal.