Shannon-Type Sampling Theory on Unions of Equally Spaced and Noncommensurate Grids

Report No. ARL-TR-2305
Authors: Terrence J. Moore
Date/Pages: February 2001; 47 pages
Abstract: Sampling theory is that branch of mathematics that seeks to reconstruct functions from its values at a discrete set of points. The fundamental result in sampling theory known as "Shannon's sampling theorem" has many applications to signal processing and communications engineering. I demonstrate Shannon's result via complex interpolation methods. I then quote a result that uses these methods to solve interpolation problems on unions of noncommensurate lattices, which are created via a specific number of theoretic guidelines. These interpolations give Shannon-type reconstructions on these lattices. I close by doing simulations in MATLAB of the sampling constructions on these noncommensurate grids.
Distribution: Approved for public release
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Last Update / Reviewed: February 1, 2001