Row-shift corrected truncation of paraunitary matrices for PEVD algorithms

Corr, Jamie and Thompson, Keith and Weiss, Stephan and Proudler, Ian K. and McWhirter, John G. (2015) Row-shift corrected truncation of paraunitary matrices for PEVD algorithms. In: 23rd European Signal Processing Conference. IEEE, pp. 849-853. ISBN 978-0-9928626-3-3

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Abstract

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.