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

This paper 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 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'nikovShannon expansions to ensure the approximation of the subGaussian signals with given accuracy and reliability. Some numerical examples are presented.