Stochastic Modeling and Estimation of Stationary Complex-Valued Signals

This paper provides a stochastic modeling framework for the power spectral representations of stationary complex-valued signals. We specify how complex-valued signals can be modeled stochastically in terms of their rotary components, which decompose a bivariate signal according to direction of rotation. The necessary relationships are provided to map between complex-rotary and bivariate-Cartesian representations. We demonstrate how by modeling in rotary components we can infer useful features from application datasets---in particular for capturing the improper or anisotropic structure of a signal---by implementing our methodology on fluid dynamic simulations of turbulence. In addition, we detail how parameters of a chosen stochastic model can be efficiently estimated in the frequency domain, by extending the Whittle likelihood to complex-valued signals. We also provide a new method of testing for complex structure such as impropriety, as well as procedures for model choice and semi-parametric modeling.