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arXiv · 2410.03667

Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals

Nikolai Dokuchaev
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Abstract

The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem for unbounded non-decaying band-limited signals. An explicit interpolation formula is obtained for signals sublinear growth with rate of growth less than 1/2. At any time, the rate of decay for the $k$th coefficients of this formula is $\sim 1/k^2$. In addition, the paper obtains a method for calculating the coefficients of the interpolation formula applicable to signals with arbitrarily high rate of polynomial growth.

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Nikolai Dokuchaev. 2024-09-12. Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals. https://arxiv.org/abs/2410.03667

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