Extraction of analytic singular values of a polynomial matrix

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.