Continuous empirical wavelets systems

TL;DR

This paper develops a general framework for continuous empirical wavelet systems, extending previous filter-based methods and providing conditions for reconstruction, with constructions based on classic mother wavelets.

Contribution

It introduces a formalism for continuous empirical wavelet systems and explores their properties, including reconstruction conditions, advancing the theoretical foundation of empirical wavelet analysis.

Findings

Established sufficient conditions for wavelet system reconstruction.

Proposed constructions based on classic mother wavelets.

Extended empirical wavelet theory to continuous settings.

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.