TY - JOUR AU - de Oliveira, H. M. AU - Falk, T. H. AU - Távora, R. F. G. PY - 2017/05/18 Y2 - 2024/03/28 TI - Decomposição de Wavelets sobre Corpos Finitos JF - Journal of Communication and Information Systems JA - Journal of Communication and Information Systems VL - 17 IS - 1 SE - Regular Papers DO - 10.14209/jcis.2002.7 UR - https://jcis.sbrt.org.br/jcis/article/view/478 SP - 38-47 AB - 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-splines over GF(p) are also considered. A few examples of multiresolution analysis over finite fields as well as conditions for the coefficients of the smoothing filter to achieve vanishing moments are presented. A new fast algorithm to compute FF-wavelets, based on a two-phase decomposition is introduced. Wavelet packed transforms over finite fields are also considered. An application of FF-wavelets to design multiplex schemes with spread-spectrum sequences is presented. ER -