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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.
Original language  English 

Pages  15 
Number of pages  5 
Publication status  Epub ahead of print  4 Sept 2023 
Event  31st European Signal Processing Conference  Helsinki, Finland Duration: 4 Sept 2023 → 8 Sept 2023 https://eusipco2023.org/ 
Conference
Conference  31st European Signal Processing Conference 

Abbreviated title  EUSIPCO'23 
Country/Territory  Finland 
City  Helsinki 
Period  4/09/23 → 8/09/23 
Internet address 
Keywords
 the Procrustes problem
 paraunitary matrices
 paraunitary matrix
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 1 Active

Signal Processing in the Information Age (UDRC III)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research