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

Adam M. Sykulski; Donald B. Percival

doi:10.1109/mlsp.2016.7738840

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arXiv · 1605.05278

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

Adam M. Sykulski·Donald B. Percival

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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 $\mathcal{O}(n\log_2 n)$ 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 $n$, with an improper fractional Gaussian noise process.

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Adam M. Sykulski, Donald B. Percival. 2016-05-17. Exact Simulation of Noncircular or Improper Complex-Valued Stationary Gaussian Processes using Circulant Embedding. https://doi.org/10.1109/mlsp.2016.7738840

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