Extracting analytic singular values from a polynomial matrix
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-06-01
|
| Series: | Science Talks |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2772569325000349 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849434369332084736 |
|---|---|
| author | Faizan A. Khattak Mohammed Bakhit Ian K. Proudler Stephan Weiss |
| author_facet | Faizan A. Khattak Mohammed Bakhit Ian K. Proudler Stephan Weiss |
| author_sort | Faizan A. Khattak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-eec0e2d2b9564725828339a9a9fd3725 |
| institution | Kabale University |
| issn | 2772-5693 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Science Talks |
| spelling | doaj-art-eec0e2d2b9564725828339a9a9fd37252025-08-20T03:26:39ZengElsevierScience Talks2772-56932025-06-011410045210.1016/j.sctalk.2025.100452Extracting analytic singular values from a polynomial matrixFaizan A. Khattak0Mohammed Bakhit1Ian K. Proudler2Stephan Weiss3Dept. of Electronic & Electrical Eng., University of Strathclyde, Glasgow, Scotland, UKCorresponding author.; Dept. of Electronic & Electrical Eng., University of Strathclyde, Glasgow, Scotland, UKDept. of Electronic & Electrical Eng., University of Strathclyde, Glasgow, Scotland, UKDept. of Electronic & Electrical Eng., University of Strathclyde, Glasgow, Scotland, UKA 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.http://www.sciencedirect.com/science/article/pii/S2772569325000349Analytic singular value decompositionPolynomial matrix decompositionsBroadband MIMO system decoupling |
| spellingShingle | Faizan A. Khattak Mohammed Bakhit Ian K. Proudler Stephan Weiss Extracting analytic singular values from a polynomial matrix Science Talks Analytic singular value decomposition Polynomial matrix decompositions Broadband MIMO system decoupling |
| title | Extracting analytic singular values from a polynomial matrix |
| title_full | Extracting analytic singular values from a polynomial matrix |
| title_fullStr | Extracting analytic singular values from a polynomial matrix |
| title_full_unstemmed | Extracting analytic singular values from a polynomial matrix |
| title_short | Extracting analytic singular values from a polynomial matrix |
| title_sort | extracting analytic singular values from a polynomial matrix |
| topic | Analytic singular value decomposition Polynomial matrix decompositions Broadband MIMO system decoupling |
| url | http://www.sciencedirect.com/science/article/pii/S2772569325000349 |
| work_keys_str_mv | AT faizanakhattak extractinganalyticsingularvaluesfromapolynomialmatrix AT mohammedbakhit extractinganalyticsingularvaluesfromapolynomialmatrix AT iankproudler extractinganalyticsingularvaluesfromapolynomialmatrix AT stephanweiss extractinganalyticsingularvaluesfromapolynomialmatrix |