Whittaker-Kotel'nikov-Shannon approximation of $\varphi$-sub-Gaussian random processes

TL;DR

This paper extends classical sampling theorem results to $\

Contribution

It introduces new truncation error bounds for approximating $\

Findings

Established explicit upper bounds for sampling approximation errors.

Generalized classical results to $\

Provided verifiable conditions for the bounds.

Abstract

The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates $L_p([0,T])$ and uniform approximations of $\varphi$-sub-Gaussian random processes by finite time sampling sums. Explicit truncation error upper bounds are established. Some specifications of the general results for which the assumptions can be easily verified are given. Direct analytical methods are employed to obtain the results.