Polynomial Procrustes problem : paraunitary approximation of matrices of analytic functions

Weiss, Stephan and Schlecht, Sebastian J. and Das, Orchisama and de Sena, Enzo (2023) Polynomial Procrustes problem : paraunitary approximation of matrices of analytic functions. In: 31st European Signal Processing Conference, 2023-09-04 - 2023-09-08.

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Abstract

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.

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