Angular parametrization of rectangular paraunitary matrices

Didier Pinchon (1) , Pierre Siohan (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this preprint a new approach is proposed to find efficient angular parametrizations of rectangular paraunitary matrices (PU). As for square PU matrices, the problem is stated as a matrix factorization, the efficiency of which is ensured by the fact that the proposed representations are complete, non redundant and lead to a minimal number of delays. As in our previous publication, dedicated to the case of square real coefficients PU matrices, our framework is based on an \emph{ensemblist} approach. The angular parametrization sets, named Givens sets, are analyzed according to three different possibilities related to the matrix size. Thus, for a NxM PU matrix, different properties of Givens sets are established corresponding to the cases where N=M, N >= 2 M and M < N < 2M.

Mots clés: Cosine-Sine Decomposition (CSD); Paraunitary matrix; polynomial matrix; QR matrix decomposition; singular value decomposition (SVD); SO(N) group

Domaines: Mathématiques [math]; Traitement du signal et de l'image [eess.SP]

Didier Pinchon, Pierre Siohan. Angular parametrization of rectangular paraunitary matrices. 2016. ⟨hal-01289570⟩