  A novel representation of functions, called generalized Taylor form, is
applied to the filtering of white noise processes. It is shown that every
Gaussian colored noise can be expressed as the output of a set of linear
fractional stochastic differential equation whose solution is a weighted sum of
fractional Brownian motions. The exact form of the weighting coefficients is
given and it is shown that it is related to the fractional moments of the
target spectral density of the colored noise.
