English

On Wavelet Decomposition over Finite Fields

Information Theory 2020-06-01 v1 math.IT Number Theory

Abstract

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.

Cite

@article{arxiv.1502.01877,
  title  = {On Wavelet Decomposition over Finite Fields},
  author = {H. M. de Oliveira and T. H. Falk},
  journal= {arXiv preprint arXiv:1502.01877},
  year   = {2020}
}

Comments

4 pages, 1 figure. conference: XIX Simposio Brasileiro de Telecomunicacoes, 2001, Fortaleza, CE, Brazil

R2 v1 2026-06-22T08:23:44.328Z