Mother wavelet functions generalized through q-exponentials

Details Mother wavelet functions generalized through q-exponentials Mother wavelet functions generalized through q-exponentials

2004-03-26

arxiv.org/abs/cond-mat/0403644v2

J. Phys. A: Math. Gen. 37, 9125--9137 (2004)

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 23 pages, 7 figures (13 eps files), new version to be published in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/37/39/006

We 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.

Affiliated with

Also associated with

No associations

Rating

Mother wavelet functions generalized through q-exponentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mother wavelet functions generalized through q-exponentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mother wavelet functions generalized through q-exponentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-383381