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Aliasing-truncation errors in sampling approximations of sub-Gaussian signals

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posted on 2025-05-29, 07:07 authored by Y Kozachenko, Andriy OlenkoAndriy Olenko
This paper starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates Lp([0,T]) approximations of the 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 the sub-Gaussian signals with given accuracy and reliability. Some numerical examples are presented.

Funding

This work was supported in part by the Australian Research Council's Discovery Projects Funding Scheme under Project DP160101366 and in part by La Trobe University DRP Grant in Mathematical and Computing Sciences.

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History

Publication Date

2016-10-01

Journal

IEEE Transactions on Information Theory

Volume

62

Issue

10

Pagination

8p. (p. 5831-5838)

Publisher

IEEE

ISSN

0018-9448

Rights Statement

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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