Estimation of the self-similarity parameter using the wavelet transform

Soltani, Skander; Simard, Patrice; Boichu, D.

doi:10.1016/j.sigpro.2003.05.002

Cited by 24 publications

(21 citation statements)

References 12 publications

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“…A powerful method was proposed in the late 1980s to perform time-scale analysis of signals: the wavelet transforms (WT). This method provides a unified framework for different techniques that have been developed for various applications (Adeli, Zhou, &, Dadmehr, 2003;Basar, Schurmann, Demiralp, Basar-Eroglu, & Ademoglu, 2001;Folkers, Mosch, Malina, & Hofmann, 2003;Geva, & Kerem, 1998;Hazarika, Chen, Tsoi, & Sergejer, 1997;Kalayci, & Ozdamar, 1995;Khan, & Gotman, 2003;Patwardhan, Dhawan, & Relue, 2003;Petrosian, Prokhorov, Homan, Dashei, & Wunsch, 2000;Quiroga, Sakowitz, Basar, & Schurmann, 2001;Quiroga, & Schurmann, 1999;Rosso, Blanco, & Rabinowicz, 2003;Rosso, Martin, & Plastino, 2002;Samar, Bopardikar, Rao, & Swartz, 1999;Soltani, Simard, & Boichu, 2004;Zhang, Kawabata, & Liu, 2001). It should also be emphasized that the WT is appropriate for analysis of non-stationary signals, and this represents a major advantage over spectral analysis.…”

Section: Introductionmentioning

confidence: 99%

Epileptic seizure detection using dynamic wavelet network

Subaşı

2005

Expert Systems with Applications

167

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Section: Introductionmentioning

confidence: 99%

Epileptic seizure detection using dynamic wavelet network

Subaşı

2005

Expert Systems with Applications

167

View full text Add to dashboard Cite

“…Equation (7) has been used for the estimation of the fractality exponent α [32] and also for computing wavelet-based information tools [14,24,25,[42][43][44]. For further information on wavelets and in the wavelet analysis of fractal signals refer to [32,33,39,40,[45][46][47][48][49] and references therein.…”

Section: The Representation Of Fractal Signals By Waveletsmentioning

confidence: 99%

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

Ramírez-Pacheco

Trejo-Sánchez

Cortez

et al. 2017

Entropy

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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.

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“…Wavelet analysis has been employed for the analysis and estimation of long-memory signals; special examples are the estimators of the parameter α given by Abry and Veitch [13,28], Soltani [29] and Shen [30]. For further information on the wavelet analysis of long-range dependent signals and other scaling processes, refer to [31][32][33] …”

Section: Wavelet Analysis Of Long-memory Signalsmentioning

confidence: 99%

“…DFA is a popular time-domain estimator of the parameter α and works even when the stationary or non-stationary signal has polynomial-type trends [34,35]. Wavelet-based estimators [12,13,[28][29][30], on the other hand, provide powerful, robust and fast estimation of long-memory parameter α. Like the DFA technique, it works with polynomial-type trends and other non-stationarities in the data.…”

Section: Estimators Of the Long-memory Parametermentioning

confidence: 99%

Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals

Ramírez-Pacheco

Rizo-Dominguez

Cortez

2015

Entropy

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Long-memory processes, in particular fractional Gaussian noise processes, have been applied as models for many phenomena occurring in nature. Non-stationarities, such as trends, mean level-shifts, etc., impact the accuracy of long-memory parameter estimators, giving rise to biases and misinterpretations of the phenomena. In this article, a novel methodology for the detection and location of mean level-shifts in stationary long-memory fractional Gaussian noise (fGn) signals is proposed. It is based on a joint application of the wavelet-Tsallis q-entropy as a preprocessing technique and a peak detection methodology. Extensive simulation experiments in synthesized fGn signals with mean level-shifts confirm that the proposed methodology not only detects, but also locates level-shifts with high accuracy. A comparative study against standard techniques of level-shift detection and location shows that the technique based on wavelet-Tsallis q-entropy outperforms the one based on trees and the Bai and Perron procedure, as well.

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Estimation of the self-similarity parameter using the wavelet transform

Cited by 24 publications

References 12 publications

Epileptic seizure detection using dynamic wavelet network

Epileptic seizure detection using dynamic wavelet network

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

Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals

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