Home 9 Volume 9 The Farey map exploited in the construction of a Farey mother wavelet
Open AccessArticle
The Farey map exploited in the construction of a Farey mother wavelet

Institut Superieur D’informatique Du Kef, Universit´e De Jendouba, 5 Rue Saleh Ayech, 7100 Kef, Tunisia.

Laboratory of Algebra, Number Theory and Nonlinear Analysis, Lr18es15, Department of Mathematics, Faculty of Sciences, University of Monastir, Boulevard of the Environment, 5000 Monastir, Tunisia.

Department of Mathematics, Higher Institute of Applied Mathematics and Informatics, Street of Assad Ibn Al Fourat, Kairouan 3100, Tunisia.

Department of Mathematics, Faculty of Sciences, University of Tabuk, King Faisal Road, 47512 Tabuk, Saudi Arabia.

* Corresponding Author
Annals of Communications in Mathematics 2023
, 6 (2),
118-132.
https://doi.org/10.62072/acm.2023.060205
Received: 19 May 2023 |
Accepted: 20 Jun 2023 |
Published: 30 Jun 2023

Abstract

The wavelet analysis of a function passes through its so-called wavelet transform. Such a transform is mathematically defined as a convolution product of the analyzed function with another analyzing function known as the mother wavelet by involving the scale and the translation parameters. This means that the mother wavelet construction is the starting and major point in the wavelet analysis. Besides, the choice of the mother wavelet remains a major problem in wavelet applications such as statistical series, time series, signal, and image processing. This needs more candidates of mother wavelets to be constructed. The main aim of the present paper is to construct a new mother wavelet by exploiting the well-known Farey map. We showed indeed that such a map may be a mother wavelet owing properties such as admissibility, moments, 2-scale relation, and reconstruction rule already necessary in the wavelet analysis of functions. By a suitable choice of translation-dilation parameters on the original Farey map, we succeeded to prove the main properties of a Farey wavelet analysis. The constructed mother looks to be suitable for many complicated applications such as hyperbolic PDEs.

Keywords

Cite This Article

The Farey map exploited in the construction of a Farey mother wavelet.

Annals of Communications in Mathematics,

2023,
6 (2):
118-132.
https://doi.org/10.62072/acm.2023.060205
  • Creative Commons License
  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

    0 Comments

    Submit a Comment

    Your email address will not be published. Required fields are marked *

    Preview PDF

    XML File

    Loading

    Share