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

A Novel Exact Representation of Stationary Colored Gaussian Processes (Fractional Differential Approach)