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

Foster, J.; McWhirter, J.G.; Davies, M.; Chambers, J.A.

doi:10.1109/tsp.2009.2034325

Cited by 53 publications

(70 citation statements)

References 11 publications

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“…McWhirter and coauthors [11] have reported the relative error of decomposition. Provided that paraunitary matrices U(z) and V(z) are of order 33, the relative error of their algorithm is 0.0469.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…This is while our algorithm only This large difference is not caused by iteration numbers because we compare results while all algorithms relatively converges, and with continuation of iterations trivial improvement are obtained. The main reason lies on different constraints of the solution presented in [11] in contrast to our proposed method. While they impose paraunitary constraint onŨ(z)A(z)V(z) to yield a diagonalized (z), we impose the finite duration constraint and obtain approximation of U(z) and V(z) with fair fitting to the decomposed matrices at each frequency samples.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…More recently, there have been much interest in polynomial matrix decomposition such as QR decomposition [10][11][12], eigenvalue decomposition (EVD) [13,14], and singular value decomposition (SVD) [5,11]. Lambert [15] has utilized Discrete Fourier transform (DFT) domain to change the problem of polynomial EVD to pointwise EVD.…”

Section: Introductionmentioning

confidence: 99%

“…Since final goal of SBR2 algorithm is to have strong decorrelation, the decomposition does not necessarily satisfy spectral majorization property. SBR2 algorithm has also been modified for QR decomposition and SVD [10,11].…”

Section: Introductionmentioning

confidence: 99%

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A DFT-based approximate eigenvalue and singular value decomposition of polynomial matrices

Tohidian

Amindavar

Azimi

2013

EURASIP J. Adv. Signal Process.

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In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices. Discrete Fourier transform enables us to propose a new algorithm based on uniform sampling of polynomial matrices in frequency domain. This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decomposition. We set up a nonlinear quadratic minimization for phase alignment of decomposition at each frequency sample, which leads to a compact order approximation of decomposed matrices. Compact order approximation of decomposed matrices makes it suitable in filterbank and multiple-input multiple-output (MIMO) precoding applications or any application dealing with realization of polynomial matrices as transfer function of MIMO systems. Numerical examples demonstrate the versatility of the proposed algorithm provided by relaxation of paraunitary constraint, and its configurability to select different properties.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A DFT-based approximate eigenvalue and singular value decomposition of polynomial matrices

Tohidian

Amindavar

Azimi

2013

EURASIP J. Adv. Signal Process.

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“…pevd-toolbox.eee.strath.ac.uk for Matlab implementations and examples). Even though the focus of this paper has been on parahermitian or polynomial EVD, the polynomial approach can also be extended to other linear algebraic factorisations such as the SVD (Foster et al, 2010;McWhirter, 2010), the QR decomposition (Foster et al, 2010;Coutts et al, 2016a) or the generalised EVD .…”

Section: Discussionmentioning

confidence: 99%

Extending Narrowband Descriptions and Optimal Solutions to Broadband Sensor Arrays

Weiss¹

2018

Proceedings of the 8th International Joint Conference on Pervasive and Embedded Computing and Communication Systems

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Abstract:This overview paper motivates the description of broadband sensor array problems by polynomial matrices, directly extending notation that is familiar from the characterisation of narrowband problems. To admit optimal solutions, the approach relies on extending the utility of the eigen-and singular value decompositions, by finding decompositions of such polynomial matrices. Particularly the factorisation of parahermitian polynomial matrices -including space-time covariance matrices that model the second order statistics of broadband sensor array data -is important. The paper summarises recent findings on the existence and uniqueness of the eigenvalue decomposition of such parahermitian polynomial matrices, demonstrates some algorithms that implement such factorisations, and highlights key applications where such techniques can provide advantages over state-of-the-art solutions.

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A Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling

Guan

Dong

Wang

et al. 2015

Latent Variable Analysis and Signal Separation

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

Cited by 53 publications

References 11 publications

A DFT-based approximate eigenvalue and singular value decomposition of polynomial matrices

A DFT-based approximate eigenvalue and singular value decomposition of polynomial matrices

Extending Narrowband Descriptions and Optimal Solutions to Broadband Sensor Arrays

A Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling

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