A class of frames for Paley-Wiener spaces with multiple lattice tiles support

Abstract

Let Ω ⊂ R^N be a bounded measurable set and let Λ ⊂ R^N be a lattice. Assume that Ω tiles R^N multiply at level K when translated by Λ. Then this paper derives conditions on sets of sampling functions such that they form a frame for the Paley-Wiener space PW_Ω of functions bandlimited to Ω. Moreover, the canonical dual frame is derived, which allows signal recovery for all signals in PW_Ω from a multichannel sampling system samples.