On a very tight truncation error bound for stationary stochastic processes

Abstract

A very tight truncation error upper bound is established for bandlimited weakly stationary stochastic processes if the sampling interval is closed. In particular, the magnitude of the upper bound is O(N/sup -2q/ ln/sup 2/ N) for a symmetric sampling reconstruction from 2N+1 sampled values, where q is an arbitrary positive integer. The results are derived with the help of the Bernstein bound on the remainder of a symmetric complex Fourier series of the function exp (i lambda t). Convergence rates are given for mean square and almost sure sampling reconstructions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>