Wavelet entropy of stochastic processes

L. ZUNINO, D. G. PÉREZ, M. GARAVAGLIA AND O. A. ROSSO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

Año: 2006 vol. 379

0378-4371

We compare two different de .nitions for the wavelet entropy associated to stochastic processes.The .rst 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.Schu ¨rmann,E.Bas -ar,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 oao 1)and fractional Brownian motion (1 oao 3)are assessed.We .nd out that the NTWS family performs better as a characterization method for these stochastic processes.-ar,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 oao 1)and fractional Brownian motion (1 oao 3)are assessed.We .nd out that the NTWS family performs better as a characterization method for these stochastic processes.oao 1)and fractional Brownian motion (1 oao 3)are assessed.We .nd out that the NTWS family performs better as a characterization method for these stochastic processes.oao 3)are assessed.We .nd out that the NTWS family performs better as a characterization method for these stochastic processes. r 2007 Elsevier B.V.All rights reserved.2007 Elsevier B.V.All rights reserved. Keywords: Wavelet analysis;Wavelet entropy;Fractional Brownian motion;Fractional Gaussian noise;a parameterWavelet analysis;Wavelet entropy;Fractional Brownian motion;Fractional Gaussian noise;a parameter