Paraunitary approximation of matrices of analytic functions - the polynomial procrustes problem
Weiss, Stephan and Schlecht, Sebastian J. and Das, Orchisama and De Sena, Enzo (2024) Paraunitary approximation of matrices of analytic functions - the polynomial procrustes problem. Science Talks. 100318. (https://doi.org/10.1016/j.sctalk.2024.100318)
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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.
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Item type: Article ID code: 88326 Dates: DateEvent27 February 2024Published27 February 2024Published Online26 February 2024AcceptedSubjects: Science > Mathematics Department: Faculty of Engineering > Electronic and Electrical Engineering
Technology and Innovation Centre > Sensors and Asset ManagementDepositing user: Pure Administrator Date deposited: 04 Mar 2024 16:31 Last modified: 03 Aug 2024 01:06 URI: https://strathprints.strath.ac.uk/id/eprint/88326