Exponential Approximation of Multivariate Bandlimited Functions from Average Oversampling
Information Theory
2014-12-23 v3 math.IT
Abstract
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an exponentially-decaying approximation error to reconstruct a multivariate bandlimited function from its finite average oversampling data. The key problem in our analysis is how to extend a function so that its Fourier transform decays at an optimal rate to zero at infinity.
Cite
@article{arxiv.1412.4265,
title = {Exponential Approximation of Multivariate Bandlimited Functions from Average Oversampling},
author = {Wenjian Chen and Haizhang Zhang},
journal= {arXiv preprint arXiv:1412.4265},
year = {2014}
}