Wavelet entropy of stochastic processes

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.