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An algorithm for calculating the QR and singular value decompositions of polynomial matrices

Foster, J. A., McWhirter, John, Davies, M. R. and Chambers, J. A. 2010. An algorithm for calculating the QR and singular value decompositions of polynomial matrices. IEEE Transactions on Signal Processing 58 (3) , pp. 1263-1274. 10.1109/TSP.2009.2034325

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Abstract

In this paper, a new algorithm for calculating the QR decomposition (QRD) of a polynomial matrix is introduced. This algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices. It is shown that this algorithm can also be used to formulate the singular value decomposition (SVD) of a polynomial matrix, which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices. Example matrices are used to demonstrate both types of decomposition. Mathematical proofs of convergence of both decompositions are also outlined. Finally, a possible application of such decompositions in multichannel signal processing is discussed.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: Convolutive mixing; multiple-input–multiple-output (MIMO) channel equalization; paraunitary matrix; polynomial matrix QR decomposition (QRD); polynomial matrix singular value decomposition (SVD)
Publisher: IEEE
ISSN: 1053-587X
Last Modified: 04 Jun 2017 02:01
URI: http://orca.cardiff.ac.uk/id/eprint/7737

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