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Abstract
A matrix of transfer functions is, in most cases, known to admit an analytic singular value decomposition (SVD), with singular values that are real-valued but potentially negative on the unit circle. In this contribution, we propose an algorithm to retrieve such analytic singular values. We propose approach operates in the frequency domain, and first computes a standard SVD of the given polynomial matrix in each discrete Fourier transform (DFT) bin. Thereafter, in order 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 can be required for analyticity. The proposed algorithm is validated through an ensemble simulation involving polynomial matrices with known analytic SVD factors.
Original language | English |
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Article number | 100452 |
Number of pages | 7 |
Journal | Science Talks |
Volume | 14 |
Early online date | 19 Mar 2025 |
DOIs | |
Publication status | E-pub ahead of print - 19 Mar 2025 |
Funding
Funding: We acknowledge support by the Commonwealth Scholarship Commission and Mathworks Ltd. The work was also in parts supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant number EP/S000631/1 and the MOD University Defence Research Collaboration in Signal Processing.
Keywords
- analytic singular value decomposition
- polynomial matrix decompositions
- broadband MIMO system decoupling
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Dive into the research topics of 'Extracting analytic singular values from a polynomial matrix'. Together they form a unique fingerprint.Projects
- 1 Finished
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Signal Processing in the Information Age (UDRC III)
Weiss, S. (Principal Investigator) & Stankovic, V. (Co-investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research
Research output
- 1 Conference contribution book
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Extraction of analytic singular values of a polynomial matrix
Khattak, F. A., Bakhit, M., Proudler, I. K. & Weiss, S., 30 Aug 2024, 32nd European Signal Processing Conference: EUSIPCO 2024. Piscataway, NJ: IEEE, p. 1297-1301 5 p. 1769Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book
Open AccessFile