Abstract
In recent years, fractional Brownian motion (FBM) model has been used in a large number of different disciplines. In the application of this model, it is imperative to estimate the Hurst parameter, which is directly related to fractal dimension . However, due to the nonstationarity of the discrete-time fractional Brownian motion (DFBM), its increment process, referred to as discrete-time fractional Gaussian noise (DFGN), is invoked as an auxiliary tool to estimate . In this dissertation, the relation between DFGN and discrete fractionally differenced Gaussian noise (fdGn) is analyzed. The relation between Hurst parameter and entropy is also derived. It is shown that the DFGN is regular. Based on the regularity, a fast and accurate method to estimate the parameter is proposed. This method possesses lower computational cost than maximum likelihood estimator (MLE) and moving average (MA) method. Furthermore, this method is robust under amplitude shift, invariant to time shift, and unaffected by a scaling factor in power spectral density (PSD). Finally, this method and the estimation of entropy embedded with Hurst parameter will be applied to the electromyogram (EMG) of external urethral sphincter (EUS). These signals come from intact rats and the injured ones from spinal cord injury (SCI). Analysis indicates that we can discriminate between intact and SCI rats from this new information.