# 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…

## One Citation

On data recovery with restraints on the spectrum range and the process range

- Computer ScienceArXiv
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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.

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