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

Foster, J. A., McWhirter, John ORCID: https://orcid.org/0000-0003-1810-3318, 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:	17 Oct 2022 10:20
URI:	https://orca.cardiff.ac.uk/id/eprint/7737

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