Factorization of Rational Function Matrices via Descriptor Representation and Its Application to the Spectral Factorization

Abstract

In this paper, the authors propose a new method of the spectral factorization. The method is based on the statespace data of a given spectral density matrix and permits one to factor it even if it has zeros on the imaginarity axis including the point at infinity. In order to develop the method, general factorization theorems for a square descriptor system is given. Then, it is shown that the spectral factorization problem is reduced to solving certain quadratic matrix equations which may be termed as generalized Riccati equation. The conditions for the existence of the solution to the equation are also derived.