Vector-valued weak Gabor dual frames on discrete periodic sets

Abstract

The notion of weak dual frames is a generalization of that of dual frames. Gabor analysis on discrete periodic sets has potential applications in signal processing. This paper addresses vector-valued weak Gabor dual frames on discrete periodic sets. We introduce the notions of its weak oblique Gabor dual, weak Gabor duals of types I and II for a Gabor system on a discrete periodic set. Using the Zak-transform matrix method, we characterize these three kinds of weak duals and their uniqueness. Finally, we give an explicit expression of a class of weak Gabor duals and provide some examples.