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metadata.dc.type: | Artigo de Periódico |
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 |
metadata.dc.creator: | Andrade, Roberto Fernandes Silva Miranda, José Garcia Vivas Tsallis, Constantino Borges, Ernesto Pinheiro |
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. |
metadata.dc.rights: | Acesso Aberto |
URI: | http://repositorio.ufba.br/ri/handle/ri/14656 |
Issue Date: | 2004 |
Appears in Collections: | Artigo Publicado em Periódico (FIS) |
Files in This Item:
File | Description | Size | Format | |
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Roberto F S Andrade.pdf | 286,11 kB | Adobe PDF | View/Open |
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