Sampling theorem for multiwavelet subspaces

Abstract

Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter’s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.