Legendre Wavelet
Compactly supported wavelets derived from Legendre polynomials are termed spherical harmonic or Legendre wavelets. Legendre functions have widespread applications in which spherical coordinate system are appropriate. As with many wavelets there is no nice analytical formula for describing these harmonic spherical wavelets. The low-pass filter associated to Legendre multiresolution analysis is a finite impulse response filter (FIR).
Wavelets associated to finite impulse response filters (FIR) are commonly preferred in most applications. An extra appealing feature is that the Legendre filters are linear phase FIR (i.e. multiresolution analysis associated with linear phase filters). These wavelets have been implemented on MATLAB (wavelet toolbox). Although being compactly supported wavelet, legdN are not orthogonal (but for N = 1).
Read more about Legendre Wavelet: Legendre Multiresolution Filters, Legendre Multiresolution Filter Coefficients, MATLAB Implementation of Legendre Wavelets, Legendre Wavelet Packets
Famous quotes containing the word wavelet:
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)