A New Multichannel Spectral Factorization Algorithm for Parahermitian Polynomial Matrices

Abstract—A novel multichannel spectral factorization algorithm is illustrated in this paper. This new algorithm is based on an iterative method for polynomial eigenvalue decomposition (PEVD) called the second order sequential best rotation (SBR2) algorithm [1]. By using the SBR2 algorithm, multichannel spectral factorization problems are simply broken down to a set of single channel problems which can be solved by means of existing one dimensional spectral factorization algorithms. In effect, it transforms the multichannel spectral factorization problem into one which is much easier to solve. The proposed algorithm can be used to calculate the approximate spectral factor of any parahermitian polynomial matrix. Two worked examples are presented in order to demonstrate its ability to find a valid spectral factor, and indicate the level of accuracy which can be achieved.