On Wavelet Decomposition over Finite Fields

H. M. de Oliveira; T. H. Falk

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arXiv · 1502.01877

On Wavelet Decomposition over Finite Fields

H. M. de Oliveira·T. H. Falk

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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.

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H. M. de Oliveira, T. H. Falk. 2015-02-06. On Wavelet Decomposition over Finite Fields. https://arxiv.org/abs/1502.01877

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