Fractal extraction from a mixed fBm signal using discrete wavelet transforms

Abstract

Since stationarity, ergodicity and self-similarity for the discrete wavelet transform of fractional Brownian motion (fBm) processes have been shown in previous works, these characteristics could be applied to extract the parameters of two fBm signals from a mixed fBm signal using time-average correlation functions. The goal of this paper is to distinguish the two identical power fBm signals from the mixed signal. In this case, we suppose that the mixed signal is available, but information on the parameters of the two fBm signals is not provided. A method is proposed to find the parameters of these two fBm signals. The smaller parameter can be detected from the fractal dimension of the mixed fBm signal. The parameter of the other fBm is estimated by processing the wavelet coefficients of the mixed fBm signal. Finally, the simulation results showed that this approach works well in increasing the difference between the parameters of the two fBms.