On fast generation of fractional Gaussian noise

A fast method of generating fractional Gaussian noise processes based on a power spectrum function is presented. Algorithms based on the fast Fourier transform reveal low computational complexity and good performance when compared to other methods of generating self-similar processes. These methods have good accuracy in that the results of estimation of Hurst exponent do not differ significantly from expected values. The aim is to improve the efficiency of Paxson's and other recent methods while keeping a high level of accuracy. The results of numerical simulations are presented and compared from the point of view of accuracy and running time. Furthermore, a new way of exact approximation of power spectrum based on the generalized Riemann zeta function is introduced. Subsequently, this method is used for accuracy evaluation of aforementioned generators.