SPECTRAL FACTORIZATION OF RANK-DEFICIENT RATIONAL DENSITIES

Though there are hundreds of papers on rational spectral factorization, most of them are concerned with full -rank spectral densities. In this paper we propose a novel approach for spectral factorization of a rank -deficient spectral density, leading to a minimum -phase full -rank spectral factor, in both the discrete -time and continuous -time cases. Compared with several approaches to low -rank spectral factorization, our approach exploits a deterministic relation inside the factor, leading to high computational efficiency. In addition, we show that this method is easily used in identification of low -rank processes and in Wiener filtering.