  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.
