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Mathematics of Computation

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A generalized sampling theorem for locally compact abelian groups

Author: Adel Faridani
Journal: Math. Comp. 63 (1994), 307-327
MSC: Primary 43A25; Secondary 65Dxx, 65T20, 94A05
MathSciNet review: 1240658
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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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Keywords: Sampling theorem, nonuniform sampling, multidimensional sampling, periodic sampling, bunched sampling, lattice rules, locally compact abelian groups
Article copyright: © Copyright 1994 American Mathematical Society