A generalized sampling theorem for locally compact abelian groups
نویسنده
چکیده
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 non-equidistant but periodic sampling on the real line. For non-bandlimited functions an L1-type estimate for the aliasing error is given. We discuss the application of the theorem to a class of sampling sets in Rs; give a general algorithm for 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. 1991 Mathematics Subject Classification: Primary: 65T99, 65D30, 94A05, 43A25; Secondary: 65D05, 65D32, 65T20, 42B99
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تاریخ انتشار 1994