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arXiv · 1204.0992

Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces

Brad Osgood·Aditya Siripuram·William Wu
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Abstract

We study the problem of interpolating all values of a discrete signal f of length N when d<N values are known, especially in the case when the Fourier transform of the signal is zero outside some prescribed index set J; these comprise the (generalized) bandlimited spaces B^J. The sampling pattern for f is specified by an index set I, and is said to be a universal sampling set if samples in the locations I can be used to interpolate signals from B^J for any J. When N is a prime power we give several characterizations of universal sampling sets, some structure theorems for such sets, an algorithm for their construction, and a formula that counts them. There are also natural applications to additive uncertainty principles.

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Brad Osgood, Aditya Siripuram, William Wu. 2012-04-04. Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces. https://doi.org/10.1109/tit.2012.2193871

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