On Wavelet Decomposition over Finite Fields

This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FF-Wavelets) including FF-Haar and FF-Daubechies are derived. Non-orthogonal FF-wavelets such as B-spline over GF(p) are also considered. A few examples of multiresolution analysis over Finite fields are presented showing how to perform Laplacian pyramid filtering of finite block lengths sequences. An application of FF-wavelets to design spread-spectrum sequences is presented.
Comment: 4 pages, 1 figure. conference: XIX Simposio Brasileiro de Telecomunicacoes, 2001, Fortaleza, CE, Brazil