Spectral Factorization of Rank-Deficient Rational Densities

TL;DR

This paper introduces a new efficient method for spectral factorization of low-rank spectral densities, enabling better identification of low-rank processes and Wiener filtering, overcoming limitations of positive definite assumptions.

Contribution

It presents a novel spectral factorization approach for low-rank densities using deterministic relations, improving computational efficiency over existing methods.

Findings

High computational efficiency demonstrated

Applicable to low-rank process identification

Effective in Wiener filtering

Abstract

Though there have been hundreds of methods on solving rational spectral factorization, most of them are based on a positive definite density matrix assumption. In this work, we propose a novel approach on the spectral factorization of a low-rank spectral density, to a minimum-phase full-rank factor. Compared with other several approaches on low-rank spectral factorizations, our approach uses the deterministic relation inside a factor, leading to a high computation efficiency. In addition, we shall show that this method is easily used in identification of low-rank processes and Wiener Filter.