Title :
Approximation of Wide-Sense Stationary Stochastic Processes by Shannon Sampling Series
Author :
Boche, Holger ; Mönich, Ullrich J.
Author_Institution :
Dept. of Mobile Commun., Tech. Univ. Berlin, Berlin, Germany
Abstract :
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.
Keywords :
information theory; mean square error methods; stochastic processes; Shannon sampling series; mean square approximation error; nonsymmetric sampling series; wide sense stationary stochastic processes; Approximation error; Approximation methods; Convergence; Stochastic processes; Approximation error; Shannon sampling series; mean-square convergence; nonsymmetric sampling series; power spectral density; stochastic process; uniformly bounded; weak-sense stationary;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2080510