Extraction of Analytic Singular Values of a Polynomial Matrix
Faizan Ahmad Khattak, Mohammed Bakhit, Ian K. Proudler, Stephan Weiss · 2024
The proof of existence of an analytic singular value decomposition (SVD) has been formally established. This mo-tivates 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.