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

Yuriy Kozachenko; Andriy Olenko

doi:10.1016/j.jmaa.2016.05.052

paper

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

arXiv:1606.01062 · doi:10.1016/j.jmaa.2016.05.052

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 $φ$ -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.

23 pages, 2 figures

Whittaker-Kotel'nikov-Shannon approximation of φ-sub-Gaussian random processes

Abstract

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