Continuous empirical wavelets systems
Spectral Theory
2024-10-28 v1 Functional Analysis
Abstract
The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.
Cite
@article{arxiv.2410.19167,
title = {Continuous empirical wavelets systems},
author = {Jerome Gilles},
journal= {arXiv preprint arXiv:2410.19167},
year = {2024}
}