Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 867042, 18 pages
Research Article

Distinguishing Stationary/Nonstationary Scaling Processes Using Wavelet Tsallis 𝑞 -Entropies

1Department of Basic Sciences and Engineering, University of Caribe, 74528 Cancún, QROO, Mexico
2Department of Electrical Engineering, CINVESTAV-IPN Unidad Guadalajara, 45010 Zapopán, JAL, Mexico
3Department of Sciences and Engineering, University of Quintana Roo, 77019 Chetumal, QROO, Mexico

Received 22 July 2011; Revised 17 October 2011; Accepted 25 October 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Julio Ramirez Pacheco et al. 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.


Classification of processes as stationary or nonstationary has been recognized as an important and unresolved problem in the analysis of scaling signals. Stationarity or nonstationarity determines not only the form of autocorrelations and moments but also the selection of estimators. In this paper, a methodology for classifying scaling processes as stationary or nonstationary is proposed. The method is based on wavelet Tsallis 𝑞 -entropies and particularly on the behaviour of these entropies for scaling signals. It is demonstrated that the observed wavelet Tsallis 𝑞 -entropies of 1 / 𝑓 signals can be modeled by sum-cosh apodizing functions which allocates constant entropies to a set of scaling signals and varying entropies to the rest and that this allocation is controlled by 𝑞 . The proposed methodology, therefore, differentiates stationary signals from non-stationary ones based on the observed wavelet Tsallis entropies for 1 / 𝑓 signals. Experimental studies using synthesized signals confirm that the proposed method not only achieves satisfactorily classifications but also outperforms current methods proposed in the literature.