On distributed sampling of smooth non-bandlimited fields
Proceedings of the 3rd international symposium on Information processing in sensor networks
Limits of signal processing performance under thresholding
Signal Processing
Local and global convergence behavior of non-equidistant sampling series
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Boundedness Behavior of the Spectral Factorization for Polynomial Data in the Wiener Algebra
IEEE Transactions on Signal Processing - Part II
Error-rate characteristics of oversampled analog-to-digital conversion
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On simple oversampled A/D conversion in L2(R)
IEEE Transactions on Information Theory
Digital representations of operators on band-limited random signals
IEEE Transactions on Information Theory
A/D conversion with imperfect quantizers
IEEE Transactions on Information Theory
Single-Bit Oversampled A/D Conversion With Exponential Accuracy in the Bit Rate
IEEE Transactions on Information Theory
Unboundedness of thresholding and quantization for bandlimited signals
Signal Processing
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In this paper, we analyze the approximation behavior of sampling series, where the sample values--taken equidistantly at Nyquist rate--are disturbed either by the nonlinear threshold operator or the nonlinear quantization operator. We perform the analysis for several spaces of bandlimited signals and completely characterize the spaces for which an approximation is possible. Additionally, we study the approximation of outputs of stable linear time-invariant systems by sampling series with disturbed samples for signals in PWπ1. We show that there exist stable systems that become unstable under thresholding and quantization and that the approximation error is unbounded irrespective of how small the quantization step size is chosen. Further, we give a necessary and sufficient condition for the pointwise and the uniform convergence of the series. Surprisingly, this condition is the well-known condition for bounded-input bounded-output (BIBO) stability. Finally, we discuss the special case of finite-impulse-response (FIR) filters and give an upper bound for the approximation error.