Extracting analytic singular values from a polynomial matrix

Faizan Ahmad Khattak, Mohammed Bakhit*, Ian K. Proudler, Stephan Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number100452
Number of pages7
JournalScience Talks
Volume14
Early online date19 Mar 2025
DOIs
Publication statusE-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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