Illinois Journal of Mathematics

Relevant sampling of band-limited functions

Richard F. Bass and Karlheinz Gröchenig

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Abstract

We study the random sampling of band-limited functions of several variables. If a band-limited function with bandwidth has its essential support on a cube of volume $R^{d}$, then $\mathcal{O}(R^{d}\log R^{d})$ random samples suffice to approximate the function up to a given error with high probability.

Article information

Source
Illinois J. Math., Volume 57, Number 1 (2013), 43-58.

Dates
First available in Project Euclid: 23 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1403534485

Digital Object Identifier
doi:10.1215/ijm/1403534485

Mathematical Reviews number (MathSciNet)
MR3224560

Zentralblatt MATH identifier
1372.94378

Subjects
Primary: 94A20: Sampling theory 42C15: General harmonic expansions, frames 60E15: Inequalities; stochastic orderings 62M30: Spatial processes

Citation

Bass, Richard F.; Gröchenig, Karlheinz. Relevant sampling of band-limited functions. Illinois J. Math. 57 (2013), no. 1, 43--58. doi:10.1215/ijm/1403534485. https://projecteuclid.org/euclid.ijm/1403534485


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