D. B. Percival (1992), `Simulating Gaussian Random Processes with Specified Spectra,' Computing Science and Statistics, 24, pp. 534-8.
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(f). 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|^alpha for alpha < 0.
Davies-Harte method; Discrete Fourier transform;Biased estimator; Power law processes; Spectral synthesis method
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