• Corpus ID: 52700

# On sampling theorem with sparse decimated samples

@article{Dokuchaev2016OnST,
title={On sampling theorem with sparse decimated samples},
author={Nikolai Dokuchaev},
journal={ArXiv},
year={2016},
volume={abs/1605.00414}
}
The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function is uniquely defined by infinite two-sided s ampling series taken with a sufficient frequency. The paper shows that these band-limited functions allows an arbitrarily close uniform approximation by functions that are uniquely defined by thei r extremely sparse subsamples representing arbitrarily small fractions of one-sided equidist ant sample series with fixed oversampling parameter. In…
1 Citations

## Figures from this paper

On data recovery with restraints on the spectrum range and the process range
This short paper investigates possibility of data recovery for finite sequences with restraints on their spectrum defined by a special discretization of the spectrum range and shows that the uniqueness sets for these sequences can be singletons.

## References

SHOWING 1-10 OF 46 REFERENCES
Generalizations of the sampling theorem: Seven decades after Nyquist
Some of the less known aspects of sampling are presented, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples.
Incomplete sampling series and the recovery of missing samples from oversampled band-limited signals
• P. Ferreira
• Mathematics, Computer Science
IEEE Trans. Signal Process.
• 1992
It is shown that any finite number of missing samples can be recovered from the remaining ones, in the case of generalized Kramer sampling expansions, if an appropriate oversampling constraint is satisfied.
Sampling-50 years after Shannon
• M. Unser
• Computer Science
Proceedings of the IEEE
• 2000
The standard sampling paradigm is extended for a presentation of functions in the more general class of "shift-in-variant" function spaces, including splines and wavelets, and variations of sampling that can be understood from the same unifying perspective are reviewed.
The Shannon sampling theorem&#8212;Its various extensions and applications: A tutorial review
It has been almost thirty years since Shannon introduced the sampling theorem to communications theory. In this review paper we will attempt to present the various contributions made for the sampling
On recovering missing values in a pathwise setting
In the paper, error-free recoverability is established for classes of sequences with Z-transform vanishing at a point with a rate that can be chosen arbitrarily, and the corresponding recovering kernels are obtained explicitly.
Causal band-limited approximation and forecasting for discrete time processes
We study causal dynamic approximation in deterministic setting of non-bandlimited discrete time processes by band-limited processes. We obtain some conditions of solvability and uniqueness of a
On predicting a band-limited signal based on past sample values
It is shown how a signal-independent linear predictor of finite order can be constructed based on Chebyshev polynomials, such that the prediction error tends to zero for sampling rate exceeding the Nyquist rate.
On Recovery of Sparse Signals Via $\ell _{1}$ Minimization
• Computer Science
IEEE Transactions on Information Theory
• 2009
The results of this paper improve the existing results in the literature by weakening the conditions and tightening the error bounds and shows that signals with larger support can be recovered accurately.