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In this paper, we show that the paraunitary (PU) matrices that arise from the polynomial eigenvalue decomposition (PEVD) of a parahermitian matrix are not unique. In particular, arbitrary shifts (delays) of polynomials in one row of a PU matrix yield another PU matrix that admits the same PEVD. To keep the order of such a PU matrix as low as possible, we pro- pose a row-shift correction. Using the example of an iterative PEVD algorithm with previously proposed truncation of the PU matrix, we demonstrate that a considerable shortening of the PU order can be accomplished when using row-corrected truncation.
- paraunitary matrices
- row-shift correction
- polynomial eigenvalue decomposition