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

Authors:
Donald B. Percival
Affiliations:
Applied Physics Laboratory, University of Washington, Seattle, WA
Venue:
Signal Processing
Year:
2006

Citing 3
Cited 1

Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix

SIAM Journal on Scientific Computing
Surrogate time series

Physica D
Simulation of stationary Gaussian vector fields

Statistics and Computing

Fast and exact synthesis of stationary multivariate Gaussian time series using circulant embedding

Signal Processing

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Abstract

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.