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Wavelet Fisher’s Information Measure of 1=f α Signals
Department of Electrical Engineering, CINVESTAV-IPN Unidad Guadalajara, 45015 Av. Cienífica 1145, Col. El Bajío, Zapopán, Jalisco, México
Department of Basic Sciences and Engineering, University of Caribe, 77528, SM-78, Mza-1, Lote-1, Esquina Fracc. Tabachines, Cancún, Q.Roo, México
* Author to whom correspondence should be addressed.
Received: 6 July 2011; in revised form: 30 July 2011 / Accepted: 18 August 2011 / Published: 6 September 2011
Abstract: This article defines the concept of wavelet-based Fisher’s information measure (wavelet FIM) and develops a closed-form expression of this measure for 1=f α signals. Wavelet Fisher’s information measure characterizes the complexities associated to 1=f α signals and provides a powerful tool for their analysis. Theoretical and experimental studies demonstrate that this quantity is exponentially increasing for α > 1 (non-stationary signals) and almost constant for α < 1 (stationary signals). Potential applications of wavelet FIM are discussed in some detail and its power and robustness for the detection of structural breaks in the mean embedded in stationary fractional Gaussian noise signals studied.
Keywords: 1=f α processes; structural breaks; Fisher information; fractal index estimation; fractional Gaussian noise
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Ramírez-Pacheco, J.; Torres-Román, D.; Rizo-Dominguez, L.; Trejo-Sanchez, J.; Manzano-Pinzón, F. Wavelet Fisher’s Information Measure of 1=f α Signals. Entropy 2011, 13, 1648-1663.
Ramírez-Pacheco J, Torres-Román D, Rizo-Dominguez L, Trejo-Sanchez J, Manzano-Pinzón F. Wavelet Fisher’s Information Measure of 1=f α Signals. Entropy. 2011; 13(9):1648-1663.
Ramírez-Pacheco, Julio; Torres-Román, Deni; Rizo-Dominguez, Luis; Trejo-Sanchez, Joel; Manzano-Pinzón, Francisco. 2011. "Wavelet Fisher’s Information Measure of 1=f α Signals." Entropy 13, no. 9: 1648-1663.