A sum of sinusoids with random phase angle and a prescribed power spectral density to approximate fractional Gaussian noise

This paper shows that V. Paxson's "quack like a duck" approach to generating fractional Gaussian noise (see Computer Communication Review, vol.27, no.5, p.5-18, 1997) is essentially a Monte Carlo procedure using a sum of sinusoids with random phase angle and a prescribed power spectral density. It is well known that a sum of sinusoids with random phase angle is a good approximation to generate a Gaussian random process with a prescribed power spectral density. It is, also, relatively fast to generate noise data when a fast Fourier transform algorithm is used. A recently developed analytical expression by D.Daut and M. Yu (see 1999 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing-PACRIM 1999, p.14-17, 1999) for the power spectral density of fractional Gaussian noise is incorporated into the procedure to avoid the use of any approximation as required in previous methods. Thus, this improved procedure should be simpler to use and should be potentially faster.