Extraction of analytic singular values of a polynomial matrix

Khattak, Faizan Ahmad 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, 2024-08-26 - 2024-08-30, Lyon Convention Centre. (In Press)

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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 a singular value extraction 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 may become negative, which is required for analyticity. The proposed algorithm is validated through an ensemble of polynomial matrices with known analytic SVD.

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