Average sampling of band-limited stochastic processes

TL;DR

This paper investigates the reconstruction of band-limited wide sense stationary stochastic processes from local average samples taken at or above the Nyquist rate, providing conditions for mean square and almost sure convergence.

Contribution

It introduces sufficient conditions for average sampling expansions in mean square and almost sure sense for band-limited stochastic processes, including analysis of errors.

Findings

Sampling expansions hold under specified conditions

Truncation and aliasing errors are characterized

Reconstruction is feasible from local averages at or above Nyquist rate

Abstract

We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions hold in mean square and for almost all sample functions. Truncation and aliasing errors of the expansion are also discussed.