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

Sykulski, AM; Olhede, SC; Lilly, JM; Early, JJ; (2017) Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals. IEEE Transactions on Signal Processing , 65 (12) pp. 3136-3151. 10.1109/TSP.2017.2686334. Green open access

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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.

Type: Article
Title: Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TSP.2017.2686334
Publisher version: http://dx.doi.org/10.1109/TSP.2017.2686334
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Technology, Engineering, Electrical & Electronic, Engineering, Time series analysis, spectral analysis, parametric statistics, stochastic processes, parameter estimation, maximum likelihood estimation, VECTOR TIME-SERIES, HYPOTHESES, STATISTICS, SELECTION, SPECTRUM, SYSTEMS, NOISE
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/10051920
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