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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.
|Number of pages||5|
|Publication status||E-pub ahead of print - 4 Sept 2023|
|Event||31st European Signal Processing Conference - Helsinki, Finland|
Duration: 4 Sept 2023 → 8 Sept 2023
|Conference||31st European Signal Processing Conference|
|Period||4/09/23 → 8/09/23|
- the Procrustes problem
- paraunitary matrices
- paraunitary matrix
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