TY - JOUR
T1 - Wavelet entropy of stochastic processes
AU - Zunino, L.
AU - Pérez, D. G.
AU - Garavaglia, M.
AU - Rosso, O. A.
N1 - Funding Information:
This work was partially supported by Consejo Nacional de Investigaciones Científicas y Técnicas (PIP 5687/05, CONICET, Argentina), Comisión Nacional de Investigación Científica y Tecnológica (CONICYT, FONDECYT Project No. 11060512, Chile), and Pontificia Universidad Católica de Valparaíso (PUCV, Project No. 123.786/2006, Chile). D.G.P. and O.A.R. are very grateful to Prof. Dr. Javier Martínez-Mardones for his kind hospitality at Instituto de Física, Pontificia Universidad Católica de Valparaíso, Chile, where part of this work was done.
PY - 2007/6/15
Y1 - 2007/6/15
N2 - We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (- 1 < α < 1) and fractional Brownian motion (1 < α < 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.
AB - We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (- 1 < α < 1) and fractional Brownian motion (1 < α < 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.
KW - Fractional Brownian motion
KW - Fractional Gaussian noise
KW - Wavelet analysis
KW - Wavelet entropy
KW - α-parameter
UR - http://www.scopus.com/inward/record.url?scp=34247543875&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2006.12.057
DO - 10.1016/j.physa.2006.12.057
M3 - Article
AN - SCOPUS:34247543875
SN - 0378-4371
VL - 379
SP - 503
EP - 512
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 2
ER -