Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 867042, 18 pages doi:10.1155/2012/867042 Research Article Distinguishing Stationary/Nonstationary Scaling Processes Using Wavelet Tsallis q-Entropies Julio Ramirez Pacheco, 1 Deni Torres Rom´ an, 2 and Homero Toral Cruz 3 1 Department of Basic Sciences and Engineering, University of Caribe, 74528 Canc ´ un, QROO, Mexico 2 Department of Electrical Engineering, CINVESTAV-IPN Unidad Guadalajara, 45010 Zapop´ an, JAL, Mexico 3 Department of Sciences and Engineering, University of Quintana Roo, 77019 Chetumal, QROO, Mexico Correspondence should be addressed to Julio Ramirez Pacheco, jramirez@ucaribe.edu.mx Received 22 July 2011; Revised 17 October 2011; Accepted 25 October 2011 Academic Editor: Carlo Cattani Copyright q 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. 1. Introduction The theory of scaling processes has shown to be meaningful in several fields of applied science 1. Some aspects of scaling behaviour have been reported in finance 2, 3, in the analysis of heart rate variability and EEGs in physiology 4, 5, in the characterization of mood and other behavioural variables in psychology 6, in the modelling of computer network traffic and delays in LANs and WANs 7, 8, and in the study of the velocity field of turbulent flows in turbulence 9–12 among others. The scaling signals studied in these fields can be modelled by a wide variety of stochastic processes, the majority of which are characterized by the single scaling index α or the associated Hurst index H. Theoretically, the