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Title: An algorithm for calculating the QR and singular value decompositions of polynomial matrices
Authors: Foster, Joanne
McWhirter, John
Davies, Martin
Chambers, Jonathon
Keywords: Convolutive mixing
Multiple-input–multiple-output (MIMO) channel equalization
Paraunitary matrix
Polynomial matrix QR decomposition (QRD)
Polynomial matrix singular value decomposition (SVD)
Issue Date: 2009
Publisher: © IEEE
Citation: FOSTER, J....et al., 2009. An algorithm for calculating the QR and singular value decompositions of polynomial matrices. IEEE Transactions on Signal Processing, 58(3), pp. 1263-1274.
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.
Description: This article was published in the journal IEEE Transactions on Signal Processing [© IEEE] and is also available at: http://ieeexplore.ieee.org/. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Version: Accepted for publication
DOI: 10.1109/TSP.2009.2034325
URI: https://dspace.lboro.ac.uk/2134/5944
ISSN: 1053-587X
Appears in Collections:Published Articles (Mechanical, Electrical and Manufacturing Engineering)

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