Simulating Gaussian Random Processes with Specified Spectra

Abstract---We discuss the problem of generating realizations of length N from a Gaussian stationary process {Y t } with a specified spectral density function S Y (·). We review three methods for generating the required realizations and consider their relative merits. In particular, we discuss an approximate frequency domain technique that is evidently used frequently in practice, but that has some potential pitfalls. We discuss extensions to this technique that allow it to be used to generate realizations from a power-law process with spectral density function similar to S(f) = |f | # for # < 0. I. Introduction Let {Y t } be a real-valued Gaussian stationary process with spectral density function (sdf) S Y (·), autocorrelation sequence (acvs) {s #,Y } and zero mean. If we define the sampling time between observations Y t and Y t+1 to be unity so that the Nyquist frequency is 1 2 , then the acvs is related to the sdf via the usual relationship s #,Y = Z 1 2 - 1 2..