Wavelet Packets Based Parameter Estimation of Fractional Brownian Motion Processes with Application

Abstract

Correlation structure of wavelet packets will be derived first. Then it will be proved that for fractional Brownian motion (fBm) processes, correlation coefficients will decrease exponentially across the wavelet packets scales-in other words almost KL-expansion. Based on the derived theorem, it is possible to estimate the parameters of fBm processes. Flexibility of the wavelet packet structure permits us to choose the bases accordingly. Simulation results show that utilizing wavelet packets it is possible to get better estimate with fewer computation than wavelet based estimation counterpart. Further application on extraction of voice signal embedded in 1/f noise will also be given.