A generalized sampling theorem for locally compact abelian groups

Faridani, Adel

doi:10.1090/S0025-5718-1994-1240658-6

A generalized sampling theorem for locally compact abelian groups
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Math. Comp. 63 (1994), 307-327 Request permission

Abstract:

We present a sampling theorem for locally compact abelian groups. The sampling sets are finite unions of cosets of a closed subgroup. This generalizes the well-known case of nonequidistant but periodic sampling on the real line. For nonbandlimited functions an ${L_1}$-type estimate for the aliasing error is given. We discuss the application of the theorem to a class of sampling sets in ${{\mathbf {R}}^s}$, give a general algorithm for a computer implementation, present a detailed description of the implementation for the s-dimensional torus group, and point out connections to lattice rules for numerical integration.

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