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.