Planar sampling sets for the short-time Fourier transform
Classical Analysis and ODEs
2019-06-10 v1 Complex Variables
Functional Analysis
Abstract
This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling bound in the case of Hermite windows and derive a sufficient condition for a large class of windows in terms of a certain planar density. On the way, we prove a Remez-type inequality for polyanalytic functions. MSC2010: 42C40, 46E15, 46E20, 42C15
Cite
@article{arxiv.1906.02964,
title = {Planar sampling sets for the short-time Fourier transform},
author = {Philippe Jaming and Michael Speckbacher},
journal= {arXiv preprint arXiv:1906.02964},
year = {2019}
}