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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