The Farey map exploited in wavelet analysis -- Construction of an associated Farey mother wavelet

TL;DR

This paper introduces a new mother wavelet derived from the Farey map, with properties suitable for analyzing hyperbolic problems like PDEs, expanding wavelet analysis tools.

Contribution

It constructs a novel Farey map-based mother wavelet and establishes its key properties for potential application in hyperbolic PDE analysis.

Findings

The wavelet satisfies admissibility and moment conditions.

It has a valid 2-scale relation and reconstruction rule.

Potential for analyzing hyperbolic PDEs.

Abstract

In the present work the well known Farey map is exploited to consruct a new mother wavelet. Properties such as admissibility, moments, 2-scale relation and reconstruction rule have been established. The constructed mother may be a good candidate to analyze hyperbolic problems such as hyperbolic PDEs.