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 |
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 |
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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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