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

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.