Exact simulation of noncircular or improper complex-valued stationary Gaussian processes using circulant embedding

Sykulski, Adam M. and Percival, Donald B. (2016) Exact simulation of noncircular or improper complex-valued stationary Gaussian processes using circulant embedding. In: 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016 - Proceedings. IEEE Computer Society, ITA. ISBN 9781509007462

Abstract

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multi-variate Gaussian processes from the circulant embedding literature. The method can be performed in O(n log2 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.