Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals
Functional Analysis
2025-04-10 v5 Spectral Theory
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 th coefficients of this formula is . 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.
Cite
@article{arxiv.2410.03667,
title = {Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals},
author = {Nikolai Dokuchaev},
journal= {arXiv preprint arXiv:2410.03667},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2405.05566, arXiv:2405.10007