Sampling and Frequency Warping
Classical Analysis and ODEs
2017-03-07 v1 Information Theory
math.IT
Abstract
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of frequencies, the function is transformed into a band-limited one. One may then perform a decomposition in Fourier series. This process gives rise to new orthonormal bases of the Sobolev spaces H^alpha. When alpha is an integer, these orthonormal bases can be expressed in terms of Laguerre functions. We study the reconstruction and speed of convergence properties of the warping-based sampling. Besides theoretical considerations, numerical experiments are performed.
Cite
@article{arxiv.1703.01330,
title = {Sampling and Frequency Warping},
author = {Stefan Lafon and Jacques Lévy Véhel and Jacques Peyrière},
journal= {arXiv preprint arXiv:1703.01330},
year = {2017}
}
Comments
21 pages, 10 figures