Legendre Wavelet - MATLAB Implementation of Legendre Wavelets

MATLAB Implementation of Legendre Wavelets

Legendre wavelets can be easily loaded into the MATLAB wavelet toolbox -- The m-files to allow the computation of Legendre wavelet transform, details and filter are (freeware) available. The finite support width Legendre family is denoted by legd (short name). Wavelets: 'legdN'. The parameter N in the legdN family is found according to 2N=+1 (length of the MRA filters).
Legendre wavelets can be derived from the low-pass reconstruction filter by an iterative procedure (the cascade algorithm). The wavelet has compact support and finite impulse response AMR filters (FIR) are used (table 1). The first wavelet of the Legendre's family is exactly the well-known Haar wavelet. Figure 2 shows an emerging pattern that progressively looks like the wavelet's shape.

The Legendre wavelet shape can be visualised using the wavemenu command of MATLAB. Figure 3 shows legd8 wavelet displayed using MATLABTM. Legendre Polynomials are also associated with windows families.