Extraction of analytic singular values of a polynomial matrix
Khattak, Faizan A. and Bakhit, Mohammed and Proudler, Ian K. and Weiss, Stephan; (2024) Extraction of analytic singular values of a polynomial matrix. In: 32nd European Signal Processing Conference. IEEE, FRA, pp. 1297-1301. ISBN 9789464593617
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Abstract
The proof of existence of an analytic singular value decomposition (SVD) has been formally established. This motivates the need to devise an algorithm which retrieves analytic singular values that are real-valued on the unit circle. We propose a frequency domain method which first computes a standard SVD of the given polynomial matrix in each discrete Fourier transform (DFT) bin. To re-establish their association across bins, the bin-wise singular values are permuted by assessing the orthogonality of singular vectors in adjacent DFT bins. In addition, the proposed algorithm determines whether bin-wise singular value should become negative, which could be required for analyticity. The proposed algorithm is validated through an ensemble of polynomial matrices with known analytic SVD.
ORCID iDs
Khattak, Faizan A., Bakhit, Mohammed, Proudler, Ian K. and Weiss, Stephan ORCID: https://orcid.org/0000-0002-3486-7206;-
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Item type: Book Section ID code: 89652 Dates: DateEvent30 August 2024Published22 May 2024AcceptedSubjects: Science > Mathematics
Science > Mathematics > Electronic computers. Computer scienceDepartment: Faculty of Engineering > Electronic and Electrical Engineering
Technology and Innovation Centre > Sensors and Asset ManagementDepositing user: Pure Administrator Date deposited: 18 Jun 2024 15:07 Last modified: 01 Oct 2024 13:02 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/89652