Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals

Sykulski, Adam M. and Olhede, Sofia Charlotta and Lilly, Jonathan M. and Early, Jeffrey J. (2017) Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals. IEEE Transactions on Signal Processing, 65 (12). pp. 3136-3151. ISSN 1053-587X

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Abstract

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. In this paper, we provide a joint framework for all three representations in the context of frequency-domain stochastic modeling. This framework allows us to extend many established statistical procedures for bivariate vector time series to complex-valued and rotary representations. These include procedures for parametrically modeling signal coherence, estimating model parameters using the Whittle likelihood, performing semiparametric modeling, and choosing between classes of nested models using model choice. We also provide a new method of testing for impropriety in complex-valued signals, which tests for noncircular or anisotropic second-order statistical structure when the signal is represented in the complex plane. Finally, we demonstrate the usefulness of our methodology in capturing the anisotropic structure of signals observed from fluid dynamic simulations of turbulence.

Item Type:
Journal Article
Journal or Publication Title:
IEEE Transactions on Signal Processing
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2200/2208
Subjects:
ID Code:
87316
Deposited By:
Deposited On:
10 Aug 2017 13:36
Refereed?:
Yes
Published?:
Published
Last Modified:
23 Sep 2020 03:39