  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.

Methodology;Computation;Machine Learning