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.
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