Reconstruction of Bandlimited Functions from Space-Time Samples

TL;DR

This paper presents a method to reconstruct bandlimited signals from discrete space-time samples using a broad class of kernels, expanding the possibilities for signal recovery in various applications.

Contribution

It introduces a framework for reconstructing bandlimited functions from space-time samples with a wide family of kernels, generalizing previous sampling theories.

Findings

Reconstruction is possible for a wide class of kernels.

Explicit conditions on sampling sets for perfect reconstruction.

Applicable to various signal processing scenarios.

Abstract

For a wide family of even kernels $\{\varphi_u, u\in I\}$, we describe discrete sets $\Lambda$ such that every bandlimited signal $f$ can be reconstructed from the space-time samples $\{(f\ast\varphi_u)(\lambda), \lambda\in\Lambda, u\in I\}$.