Relevant Sampling of Band-limited Functions

TL;DR

This paper investigates the number of random samples needed to accurately approximate multivariable band-limited functions, showing that roughly R^d log R^d samples are sufficient for high-probability accuracy.

Contribution

It establishes a probabilistic sampling bound for multivariable band-limited functions based on their bandwidth and support volume.

Findings

Approximately R^d log R^d samples suffice for accurate approximation

Sampling complexity scales with support volume and dimension

High-probability approximation guarantees are provided

Abstract

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