Paraunitary approximation of matrices of analytic functions - the polynomial Procrustes problem
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A4 Artikkeli konferenssijulkaisussa
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Date
2024
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en
Pages
4
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Science Talks, Volume 10
Abstract
The best least squares approximation of a matrix, typically e.g. characterising gain factors in narrowband problems, by a unitary one is addressed by the Procrustes problem. Here, we extend this idea to the case of matrices of analytic functions, and characterise a broadband equivalent to the narrowband approach which we term the polynomial Procrustes problem. Its solution relies on an analytic singular value decomposition, and for the case of spectrally majorised, distinct singular values, we demonstrate the application of a suitable algorithm to three problems via simulations: (i) time delay estimation, (ii) paraunitary matrix completion, and (iii) general paraunitary approximations.Description
Keywords
Paraunitary matrix, Least squares approximation, Filter bank design, Analytic singular value decomposition, Matrix completion, Delay estimation
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Citation
Weiss, S, Schlecht, S J, Das, O & De Sena, E 2024, ' Paraunitary approximation of matrices of analytic functions - the polynomial Procrustes problem ', Science Talks, vol. 10 . https://doi.org/10.1016/j.sctalk.2024.100318