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Entropy 2017, 19(5), 224; doi:10.3390/e19050224

Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy

1
Department of Basic Sciences and Engineering, DCBeI, University of Caribe, SM-78, Mza-1, Lote-1, Esquina Fraccionamiento Tabachines, 77528 Cancún, Mexico
2
CONACYT-Centro de Investigación en Matemáticas, Carretera Sierra Papacal, Chuburna Puerto km 5, 97302 Mérida, Mexico
3
Department of Electrical Engineering, Instituto Tecnológico de Sonora, 5 de Febrero, 818 Sur, Colonia Centro, 85000 Ciudad Obregón, Mexico
4
Unidad Navojoa, Instituto Tecnológico de Sonora, Ramón Corona y Aguacalientes S/N, Col. ITSON, 85860 Navojoa, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 3 March 2017 / Revised: 28 April 2017 / Accepted: 9 May 2017 / Published: 15 May 2017
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
View Full-Text   |   Download PDF [1217 KB, uploaded 15 May 2017]   |  

Abstract

This article proposes a methodology for the classification of fractal signals as stationary or nonstationary. The methodology is based on the theoretical behavior of two-parameter wavelet entropy of fractal signals. The wavelet ( q , q ) -entropy is a wavelet-based extension of the ( q , q ) -entropy of Borges and is based on the entropy planes for various q and q ; it is theoretically shown that it constitutes an efficient and effective technique for fractal signal classification. Moreover, the second parameter q provides further analysis flexibility and robustness in the sense that different ( q , q ) pairs can analyze the same phenomena and increase the range of dispersion of entropies. A comparison study against the standard signal summation conversion technique shows that the proposed methodology is not only comparable in accuracy but also more computationally efficient. The application of the proposed methodology to physiological and financial time series is also presented along with the classification of these as stationary or nonstationary. View Full-Text
Keywords: fractal signal classification; fractional Gaussian noise/fractional Brownian motion (fGn/fBm) dichotomy; wavelets; non-extensive entropies; two-parameter entropies fractal signal classification; fractional Gaussian noise/fractional Brownian motion (fGn/fBm) dichotomy; wavelets; non-extensive entropies; two-parameter entropies
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Ramírez-Pacheco, J.C.; Trejo-Sánchez, J.A.; Cortez-González, J.; Palacio, R.R. Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy. Entropy 2017, 19, 224.

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