Compactly Supported Wavelets Derived From Legendre Polynomials: Spherical Harmonic Wavelets

TL;DR

This paper introduces a new family of compactly supported spherical harmonic wavelets derived from Legendre polynomials, utilizing differential equations and FIR filters for multiresolution analysis.

Contribution

It presents a novel construction of spherical harmonic wavelets based on Legendre polynomials, with a specific focus on their compact support and filter design.

Findings

Wavelets are associated with Legendre polynomials.

The wavelets have compact support and are derived from differential equations.

The low-pass filter is a linear phase FIR filter.

Abstract

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated with Legendre multiresolution analysis is a linear phase finite impulse response filter (FIR).