Relevant sampling of band-limited functions

2013/01/01 by Richard F. Bass, Karlheinz Gröchenig · 1 citation
Mathematics · #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Numerical methods in inverse problems #Bandlimiting #Mathematics #Sampling (signal processing) #Bandwidth (computing) #Statistics #Sampling design #Function (biology) #Random variable #Stratified sampling #Applied mathematics #Statistical physics #Computer science #Algorithm #Mathematical analysis #Physics #Telecommunications #Fourier transform

paper · pdf · doi:10.1215/ijm/1403534485

openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 O(R^dlog R^d) random samples suffice to approximate the function up to a given error with high probability.

Citations

• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty-III: The Dimension of the Space of Essentially Time- and Band-Limited Signals
• User-Friendly Tail Bounds for Sums of Random Matrices
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II

Cited by

• Kaczmarz method [wikipedia]

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