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An Algorithm for Calculating the QR and Singular Value Decompositions of Polynomial Matrices

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4 Author(s)
Foster, J.A. ; Dept. of Electron. & Electr. Eng., Loughborough Univ., Loughborough, UK ; McWhirter, J.G. ; Davies, M.R. ; Chambers, J.A.

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.

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Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 3 )