Exact simulation of complex-valued Gaussian stationary processes via circulant embedding

Circulant embedding is a technique that has been used to generate realizations from certain real-valued Gaussian stationary processes. This technique has two potential advantages over competing methods for simulating time series. First, the statistical properties of the generating procedure are exactly the same as those of the target stationary process. Second, the technique is based upon the discrete Fourier transform and hence is computationally attractive when this transform is computed via a fast Fourier transform (FFT) algorithm. In this paper we show how, when used with a standard ‘powers of two’ FFT algorithm, circulant embedding can be readily adapted to handle complex-valued Gaussian stationary processes.