On the polyanalytic short-time Fourier transform in the quaternionic setting
Complex Variables
2021-10-15 v2
Abstract
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions. Indeed, we will use the notions of true and full slice polyanalytic Fock spaces and Segal-Bargmann transforms. We prove new properties of this QSTFT including a Moyal formula, a reconstruction formula and a Lieb's uncertainty principle. These results extend a recent paper of the authors which studies a QSTFT having a Gaussian function as a window.
Cite
@article{arxiv.2110.04520,
title = {On the polyanalytic short-time Fourier transform in the quaternionic setting},
author = {Antonino De Martino and Kamal Diki},
journal= {arXiv preprint arXiv:2110.04520},
year = {2021}
}