Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces
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.
Keywords
Cite
@article{arxiv.1204.0992,
title = {Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces},
author = {Brad Osgood and Aditya Siripuram and William Wu},
journal= {arXiv preprint arXiv:1204.0992},
year = {2012}
}
Comments
24 pages, 5 figures, Accepted for publication in IEEE Transactions on Information Theory