Towards New Multiwavelets: Associated Filters and Algorithms. Part I: Theoretical Framework and Investigation of Biomedical Signals, ECG and Coronavirus Cases

TL;DR

This paper develops a theoretical framework for multiwavelets, introducing new filters and algorithms, and demonstrates their application in analyzing biomedical signals like ECG and Coronavirus data.

Contribution

It extends wavelet theory to multiwavelets with independent components, proposing new filters and algorithms, and applies them to biomedical signal processing.

Findings

Developed a generalized multiwavelet framework with independent components.

Created new filters and algorithms for multiwavelet decomposition and reconstruction.

Successfully applied the framework to ECG and Coronavirus signal analysis.

Abstract

Biosignals are nowadays important subjects for scientific researches from both theory and applications especially with the appearance of new pandemics threatening humanity such as the new Coronavirus. One aim in the present work is to prove that Wavelets may be successful machinery to understand such phenomena by applying a step forward extension of wavelets to multiwavelets. We proposed in a first step to improve the multiwavelet notion by constructing more general families using independent components for multi-scaling and multiwavelet mother functions. A special multiwavelet is then introduced, continuous and discrete multiwavelet transforms are associated, as well as new filters and algorithms of decomposition and reconstruction. The constructed multiwavelet framework is applied for some experimentations showing fast algorithms, ECG signal, and a strain of Coronavirus processing.