Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Two remarks on the reconstruction of sampled non-bandlimited functions
IBM Journal of Research and Development
Information science: Truncation error for band-limited random processes
Information Sciences: an International Journal
Irregular sampling theorems for wavelet subspaces
IEEE Transactions on Information Theory
Digital representations of operators on band-limited random signals
IEEE Transactions on Information Theory
Perturbation of Regular Sampling in Shift-Invariant Spaces for Frames
IEEE Transactions on Information Theory
Unboundedness of thresholding and quantization for bandlimited signals
Signal Processing
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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.