Extraction of analytic singular values of a polynomial matrix

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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.
Original languageEnglish
Title of host publication32nd European Signal Processing Conference
Subtitle of host publicationEUSIPCO 2024
Place of PublicationPiscataway, NJ
PublisherIEEE
Pages1297-1301
Number of pages5
ISBN (Print)9789464593617
Publication statusPublished - 30 Aug 2024
Event32nd European Signal Processing Conference - Lyon Convention Centre, Lyon, France
Duration: 26 Aug 202430 Aug 2024
https://eusipcolyon.sciencesconf.org/

Conference

Conference32nd European Signal Processing Conference
Abbreviated titleEUSIPCO'24
Country/TerritoryFrance
CityLyon
Period26/08/2430/08/24
Internet address

Keywords

  • extraction algorithms
  • singular value decomposition (SVD)
  • signal processing

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