Aliasing-truncation Errors in Sampling Approximations of Sub-Gaussian Signals

TL;DR

This paper develops new bounds for aliasing-truncation errors in sampling non-bandlimited sub-Gaussian signals, providing a constructive method to determine sampling parameters for accurate approximations.

Contribution

It introduces explicit upper bounds for aliasing-truncation errors and offers a constructive algorithm for sampling rate and sample size selection in sub-Gaussian signal approximation.

Findings

New aliasing-truncation error bounds for non-bandlimited signals

Explicit convergence rates for sub-Gaussian signal approximations

Numerical examples demonstrating the effectiveness of the proposed method

Abstract

The article starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates $L_p([0,T])$ approximations of sub-Gaussian random signals. Explicit truncation error upper bounds are established. The obtained rate of convergence provides a constructive algorithm for determining the sampling rate and the sample size in the truncated Whittaker-Kotel'nikov-Shannon expansions to ensure the approximation of sub-Gaussian signals with given accuracy and reliability. Some numerical examples are presented.