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.Keywordsspectral factorizationlow-rank processrank-deficient rational spectral densitiesfeedback representationMSC codes15A2346E2093E1193E12