### A New Multichannel Spectral Factorization Algorithm for Parahermitian Polynomial Matrices

Zeliang Wang, Johh G. McWhirter

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#### 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.

## References

[1] J. McWhirter, P. Baxter, T. Cooper, S. Redif, and J. Foster, “An EVD algorithm for para-hermitian polynomial matrices”,
*IEEE Transactions on Signal Processing*, vol. 55, no. 5, pp. 2158–2169, May 2007.