Spectral Factorization of Rank-Deficient Polynomial Matrix-Functions

TL;DR

This paper proves a spectral factorization theorem for polynomial rank-deficient matrix-functions and uses it to construct paraunitary matrix-functions with specified first rows.

Contribution

It introduces a spectral factorization theorem for rank-deficient polynomial matrix-functions and applies it to construct paraunitary matrices with given first rows.

Findings

Spectral factorization theorem established for rank-deficient polynomial matrices

Constructed paraunitary matrix-functions with prescribed first rows

Demonstrated applications in matrix-function construction

Abstract

A spectral factorization theorem is proved for polynomial rank-deficient matrix-functions. The theorem is used to construct paraunitary matrix-functions with first rows given.