47. Compactly Supported Wavelets Derived from Legendre Polynomials: Spherical Harmonic Wavelets

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 to Legendre multiresolution analysis is a linear phase
finite impulse response filter (FIR).