A New Approach to Spectral Factorization of a Class of Matrix-Valued Spectral Densities

Abstract

In this paper we propose a new approach to spectral factorization of a class of matrix-valued spectral densities. Our results are based on a recent necessary and sufficient uniform log-integrability condition for the canonical spectral factorization mapping to be sequentially continuous. In particular, we derive a new set of easily verifiable sufficient conditions for uniform log-integrability to hold. The proposed approach does not require the spectral density to be coercive, and the class to which it is applicable is reasonably large as to include many spectral densities which are of interest in applications. We also present a new spectral factorization algorithm for scalar analytic spectral densities along with a numerical example.