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Please use this identifier to cite or link to this item: http://repositorio.ufba.br/ri/handle/ri/14656

Title: Mother wavelet functions generalized through q-exponentials
Other Titles: Journal of Physics -London- a Mathematical and General
Authors: Andrade, Roberto Fernandes Silva
Miranda, José Garcia Vivas
Tsallis, Constantino
Borges, Ernesto Pinheiro
Issue Date: 2004
Abstract: We generalize somewidely usedmotherwavelets by means of the q-exponential function ex q ≡ [1 + (1 − q)x]1/(1−q) q ∈ R, ex1 = ex that emerges from nonextensive statistical mechanics. In particular, we define extended versions of the Mexican hat and the Morlet wavelets. We also introduce new wavelets that are q-generalizations of the trigonometric functions. All cases reduce to the usual ones as q → 1. Within nonextensive statistical mechanics, departures from unity of the entropic index q are expected in the presence of long-range interactions, long-term memory, multi-fractal structures, among others. Consistently the analysis of signals associated with such features is hopefully improved by proper tuning of the value of q. We exemplify with the wavelet transform modulus-maxima method for mono- and multi-fractal self-affine signals.
Description: Texto completo: acesso restrito. p. 9125–9137
URI: http://repositorio.ufba.br/ri/handle/ri/14656
ISSN: 0305-4470
Appears in Collections:Artigos Publicados em Periódicos (FIS)

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