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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 210592, 9 pages
http://dx.doi.org/10.1155/2015/210592
Research Article

Generalized Wavelet Fisher’s Information of Signals

1Department of Basic Sciences and Engineering, University of Caribe, 77528 Cancún, QROO, Mexico
2Department of Sciences and Engineering, University of Quintana Roo, 77019 Chetumal, QROO, Mexico
3Department of Electronics, Systems and Informatics, ITESO Jesuit University of Guadalajara, 45604 San Pedro Tlaquepaque, JAL, Mexico
4Engineering and Technology Department, Sonora Institute of Technology, 85000 Ciudad Obregón, SON, Mexico

Received 22 October 2014; Accepted 18 March 2015

Academic Editor: Remi Léandre

Copyright © 2015 Julio Ramírez-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.

Abstract

This paper defines the generalized wavelet Fisher information of parameter . This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for signals are determined and a detailed discussion of their properties, characteristics and their relationship with wavelet -Fisher information are given. Information planes of signals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary signals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of the F-statistic.