Mother wavelet functions generalized through q-exponentials

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dc.creatorBorges, Ernesto P.
dc.creatorTsallis, Constantino
dc.creatorMiranda, Jose G. V.
dc.creatorAndrade, Roberto F. S.
dc.date2004-03-26
dc.date2004-08-30
dc.date.accessioned2026-07-07T02:57:16Z
dc.date.available2026-07-07T02:57:16Z
dc.descriptionWe generalize some widely used mother wavelets by means of the q-exponential function $e_q^x \equiv [1+(1-q)x]^{1/(1-q)}$ ($q \in {\mathbb R}$, $e_1^x=e^x$) that emerges from nonextensive statistical mechanics. Particularly, 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 $q \to 1$. 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 WTMM Method for mono- and multi-fractal self-affine signals.
dc.descriptionLaTeX, 23 pages, 7 figures (13 eps files), new version to be published in J. Phys. A: Math. Gen
dc.identifierhttps://arxiv.org/abs/cond-mat/0403644
dc.identifierhttp://arxiv.org/abs/cond-mat/0403644
dc.identifierJ. Phys. A: Math. Gen. 37, 9125--9137 (2004)
dc.identifierdoi:10.1088/0305-4470/37/39/006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/23603
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titleMother wavelet functions generalized through q-exponentials
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