Greedy algorithm for general biorthogonal systems
Journal of Approximation Theory
On distributed sampling of smooth non-bandlimited fields
Proceedings of the 3rd international symposium on Information processing in sensor networks
Complete characterization of stable bandlimited systems under quantization and thresholding
IEEE Transactions on Signal Processing
Distributed sampling for dense sensor networks: a "Bit-conservation principle"
IPSN'03 Proceedings of the 2nd international conference on Information processing in sensor networks
Behavior of the quantization operator for bandlimited, nonoversampled signals
IEEE Transactions on Information Theory
Approximation of wide-sense stationary stochastic processes by Shannon sampling series
IEEE Transactions on Information Theory
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
Error-rate characteristics of oversampled analog-to-digital conversion
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A/D conversion with imperfect quantizers
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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It is well-known that the Shannon sampling series is locally uniformly convergent for all signals in the Paley-Wiener space PW"@p^1. An interesting question is how this good local approximation behavior is affected if the samples are disturbed by the non-linear threshold operator. This operator, which sets to zero all samples with absolute value smaller than some threshold, arises in the modeling of many applications, e.g., in wireless sensor networks. Moreover, it constitutes an essential part of a large class of quantizers, and consequently is important for all digital signal processing applications that involve conversion between analog and digital domains. In this paper, the approximation behavior of the Shannon sampling series that only uses the samples with absolute value larger than or equal to some threshold is analyzed. It is shown that there exists a signal in PW"@p^1 such that the local approximation error increases unboundedly as the threshold tends to zero. Moreover, for a fixed threshold, the local approximation error can grow arbitrarily large on the set of signals whose norm is bounded by one. With this, we generalize results of Butzer et al. that were given in the paper ''On quantization, truncation and jitter errors in the sampling theorem and its generalizations,'' Signal Processing (2) 1980 [1]. We conclude the paper with a discussion about the differences in the reconstruction behavior between the sampling series which is truncated in the domain of the sampled signal, i.e., time-domain truncation, and the sampling series which is truncated in the range of the sampled signal.