The Geometry of Sampling on Unions of Lattices

Details The Geometry of Sampling on Unions of Lattices The Geometry of Sampling on Unions of Lattices

2003-08-26

arxiv.org/abs/math/0308251v1

Mathematics

Functional Analysis

10 pages

Scientific paper

In this short note we show two results concerning sampling translation invariant subspaces of $\ltwod$ on unions of lattices. The first result shows that the sampling transform on a union of lattices is a constant times an isometry if and only if the sampling transform on each individual lattice is so. The second result demonstrates that the sampling transforms of two unions of lattices on two bands have orthogonal ranges if and only if correspondingly the sampling transforms of each pair of lattices have orthogonal ranges. We then consider sampling on shifted lattices.

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