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Approximation of Wide-Sense Stationary Stochastic Processes by Shannon Sampling Series

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2 Author(s)
Holger Boche ; Heinrich Hertz Chair for Mobile Communications, Technische Universit?t Berlin, Berlin, Germany ; Ullrich J. Monich

In this paper, the convergence behavior of the symmetric and the nonsymmetric Shannon sampling series is analyzed for bandlimited continuous-time wide-sense stationary stochastic processes that have absolutely continuous spectral measure. It is shown that the nonsymmetric sampling series converges in the mean-square sense uniformly on compact subsets of the real axis if and only if the power spectral density of the process fulfills a certain integrability condition. Moreover, if this condition is not fulfilled, then the pointwise mean-square approximation error of the nonsymmetric sampling series and the supremum of the mean-square approximation error over the real axis of the symmetric sampling series both diverge. This shows that there is a significant difference between the convergence behavior of the symmetric and the nonsymmetric sampling series.

Published in:

IEEE Transactions on Information Theory  (Volume:56 ,  Issue: 12 )