Polynomial Procrustes problem: paraunitary approximation of matrices of analytic functions

Stephan Weiss, Sebastian J. Schlecht, Orchisama Das, Enzo de Sena

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In the narrowband case, the best least squares approximation of a matrix by a unitary one is given by the Procrustes problem. In this paper, we expand this idea to matrices of analytic functions, and characterise a broadband equivalent to the narrowband case: the polynomial Procrustes problem. Its solution is based 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 — time delay estimation, paraunitary matrix completion, and general paraunitary approximations — in simulations.
Original languageEnglish
Number of pages5
Publication statusE-pub ahead of print - 4 Sept 2023
Event31st European Signal Processing Conference - Helsinki, Finland
Duration: 4 Sept 20238 Sept 2023


Conference31st European Signal Processing Conference
Abbreviated titleEUSIPCO'23
Internet address


  • the Procrustes problem
  • paraunitary matrices
  • paraunitary matrix


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