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Exact Simulation of Noncircular or Improper Complex-Valued Stationary Gaussian Processes using Circulant Embedding

17 May 2016
A. Sykulski
D. Percival
ArXiv (abs)PDFHTML
Abstract

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in O(nlog2n)\mathcal{O}(nlog_2n)O(nlog2​n) operations, where n is the length of the desired sequence. The method is exact, except when eigenvalues of prescribed circulant matrices are negative. We evaluate the performance of the algorithm empirically, and provide a practical example where the method is guaranteed to be exact for all nnn, with an improper fractional Gaussian noise process.

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