A novel method for multichannel spectral factorization

A novel algorithm for the spectral factorization (SF) of a para-Hermitian polynomial matrix (PPM) is presented. This utilizes a series of paraunitary transformations to reconstruct the spectral factors of the PPM from the spectral factors of its eigenvalue polynomial matrix (EPM). The EPM is a diagonal polynomial matrix (DPM) obtained by applying a set of simple shift and rotation operators to the PPM using the second order best rotation (SBR2) algorithm. The spectral factors of the EPM are calculated by factorizing each of its scalar elements independently. In this paper, it is shown how to generate a series of paraunitary matrices which then map the factors of the EPM to the required spectral factors of the original PPM. The method basically introduces a sequence of stable operators which provide a direct connection between the one-dimensional spectral factorization problem and the multidimensional case.