Wavelet eXtropy of fractal signals
DOI:
https://doi.org/10.31349/RevMexFisE.22.010211Keywords:
Fractal; eXtropy; wavelets; wavelet entropy; wavelet eXtropy; fractal analysisAbstract
Recently, the concept of eXtropy was proposed as a complementary dual of Shannon entropy. This article extends the standard time-domain eXtropy concept to the time-scale domain and then obtains a closed-form expression for this wavelet eXtropy for fractal signals of parameter α. A didactic study of the wavelet eXtropy of fractal signals reveals that this infomation-theory quantifier increases for short-memory fractal signals, is maximum for white noise (α = 0) and decreases for long-memory fractal processes. Compared to the standard wavelet entropy, wavelet eXtropy performs similar, however has lower variability for stationary fractal signals and higher variability for nonstationary ones. Moreover, the computation of fractality based eXtropy planes allows to highlight further properties and also potential applications for the analysis/estimation of fractals.
.
References
A.López-Lambraño, et al., Una revisión de los métodos para estimar el exponente de Hurst y la dimension fractal en series de precipitación y temperatura, Rev. Mex. Fis. 63 (2017) 244
C.-K. Peng, et al., Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (1994) 1685
M. S. Taqqu, V. Teverovsky, and W. Willinger, Estimators for long-range dependence: an empirical study, Fractals 3 (1995) 785
G. Chan, P. Hall, and D. S. Poskitt, Periodogram-based estimators of fractal properties, The Annals of Statistics (1995) 1684
D. Veitch and P. Abry, A wavelet-based joint estimator of the parameters of long-range dependence, IEEE Transactions on Information Theory 45 (1999) 878
P. Abry and D. Veitch, Wavelet analysis of longrangedependent traffic, IEEE transactions on information theory 44 (1998) 2
J. Ramírez-Pacheco et al., Wavelet Fisher’s information measure of 1/fα signals, Entropy 13 (2011) 1648
J. Ramírez-Pacheco et al., Wavelet q-Fisher information for scaling signal analysis, Entropy 14 (2012) 1478
J. C. Ramírez-Pacheco et al., Classification of fractal signals using two-parameter non-extensive wavelet entropy, Entropy 19 (2017) 224
A. Capurro et al., Tsallis entropy and cortical dynamics: the analysis of EEG signals, Physica A: statistical mechanics and its applications 257 (1998) 149
W.-X. Ren and Z.-S. Sun, Structural damage identification by using wavelet entropy, Engineering structures 30 (2008) 2840
O. Rosso, M. Martin, and A. Plastino, Brain electrical activity analysis using wavelet-based informational tools (II): Tsallis non-extensivity and complexity measures, Physica A: Statistical Mechanics and its Applications 320 (2003) 497
O. Rosso and A. Figliola, Order/disorder in brain electrical activity, Rev. Mex. Fis. 50 (2004) 149
J. C. Ramírez-Pacheco, L. Rizo-Domínguez, and J. CortezGonzalez, Wavelet-Tsallis entropy detection and location of mean level-shifts in long-memory fGn signals, Entropy 17 (2015) 7979
F. Lad, G. Sanfilippo, and G. Agro, Extropy: Complementary dual of entropy, Statistical Science 30 (2015) 40
J. Murguía and E. Campos-Cantón, Wavelet analysis of chaotic time series, Rev. Mex. Fis. 52 (2006) 155
M. Greiner et al., Wavelets: from signal analysis to the analysis of complex processes., Rev. Mex. Fis. 44 (1998) 11
J. P. L. Escola et al., The Haar wavelet transform in IoT digital audio signal processing, Circuits, Systems, and Signal Processing 41 (2022) 4174
S. Stoev et al., On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet traffic, Computer Networks 48 (2005) 423
P. Abry, D. Veitch, and P. Flandrin, Long-range dependence: Revisiting aggregation with wavelets, Journal of Time Series Analysis 19 (1998) 253
O. A. Rosso et al., Wavelet entropy: a new tool for analysis of short duration brain electrical signals, Journal of neuroscience methods 105 (2001) 65
L. Zunino et al., Wavelet entropy of stochastic processes, Physica A: Statistical Mechanics and its Applications 379 (2007) 503
J. Ramírez-Pacheco, et al., A nonextensive wavelet (q, qA´)- ˆ entropy for 1/fα signals, Rev. Mex. Fis. 62 (2016) 229
J. R. Pacheco, D. T. Roman, and H. T. Cruz, Distinguishing Stationary/ Nonstationary Scaling Processes Using Wavelet Tsallis q-Entropies., Mathematical Problems in Engineering 2012 (2012)
J. Ramírez-Pacheco and D. Torres-Roman, Cosh window behaviour of wavelet Tsallis q-entropies in 1/fα signals, Electronics Letters 47 (2011) 186
J. Liu and F. Xiao, On the maximum extropy negation of a probability distribution, Communications in Statistics-Simulation and Computation (2021) 1
Q. Zhou and Y. Deng, Belief eXtropy: Measure uncertainty from negation, Communications in Statistics-Theory and Methods (2021) 1
N. Balakrishnan, F. Buono, and M. Longobardi, On Tsallis extropy with an application to pattern recognition, Statistics and Probability Letters 180 (2022) 109241
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Julio Ramirez-Pacheco
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
