On properties and structure of the analytic singular value decomposition
Weiss, Stephan and Proudler, Ian K. and Barbarino, Giovanni and Pestana, Jennifer and McWhirter, John G. (2024) On properties and structure of the analytic singular value decomposition. IEEE Transactions on Signal Processing, 72. pp. 2260-2275. ISSN 1053-587X (https://doi.org/10.1109/TSP.2024.3387726)
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Abstract
We investigate the singular value decomposition (SVD) of a rectangular matrix A(z) of functions that are analytic on an annulus that includes at least the unit circle. Such matrices occur, e.g., as matrices of transfer functions representing broadband multiple-input multiple-output systems. Our analysis is based on findings for the analytic SVD applicable to continuous time systems, and on the analytic eigenvalue decomposition. Using these, we establish two potentially overlapping cases where analyticity of the SVD factors is denied. Firstly, from a structural point of view, multiplexed systems require oversampling by the multiplexing factor in order to admit an analytic solution. Secondly, from an algebraic perspective, we state under which condition spectral zeroes of any singular value require additional oversampling by a factor of two if an analytic solution is to be found. In all other cases, an analytic matrix admits an analytic SVD, whereby the singular values are unique up to a permutation, and the left- and right-singular vectors are coupled through a joint ambiguity w.r.t.~an arbitrary allpass function. We demonstrate how some state-of-the-art polynomial matrix decomposition algorithms approximate this solution, motivating the need for dedicated algorithms.
ORCID iDs
Weiss, Stephan ORCID: https://orcid.org/0000-0002-3486-7206, Proudler, Ian K., Barbarino, Giovanni, Pestana, Jennifer ORCID: https://orcid.org/0000-0003-1527-3178 and McWhirter, John G.;-
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Item type: Article ID code: 88703 Dates: DateEvent8 May 2024Published11 April 2024Published Online6 April 2024Accepted20 September 2023SubmittedSubjects: Technology > Electrical engineering. Electronics Nuclear engineering Department: Technology and Innovation Centre > Sensors and Asset Management
Faculty of Engineering > Electronic and Electrical Engineering
Faculty of Science > Mathematics and StatisticsDepositing user: Pure Administrator Date deposited: 15 Apr 2024 09:59 Last modified: 12 Dec 2024 15:23 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/88703