Random Processes With Specified Spectral Density and First-Order ProbabilityDensity

The procedure for generating a Gaussian random process whose power spectral density (psd) is a specified function of frequency, S(co), is well known. As we see in Fig. 1, let H(jco) be the transfer function of a linear time-invariant filter, and let the input to the filter be a Gaussian random process {jc(0} with psd Ov(w). Then the psd of the output process {.y(0} is given by