Abstract: “In this work, four different sets of data traffic have been generated from fractional brownian motion (fBm) to estimate true values of Hurst exponent boundaries in order to determine the degree of self-similarity in terms of long range dependence (LRD). One-dimensional multilevel wavelet decomposition and filtering algorithm is applied to filter fractional Gaussian noise (fGn) in the fBm generated. Autocorrelation function (ACF) and fast Fourier transform (FFT) energy spectrum is used to validate the result of the filtering effect. The result of the filtering process revealed that fGn in the fBm is de-noised successfully as the coefficient of ACF grow above zero and energy rate in the FFT- spectrum increases tremendously.”

Keywords: fBm, ACF, FFT, LRD Hurst exponent and self-similarity.