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A Widely Linear Complex Autoregressive Process of Order One

Sykulski, AM; Olhede, SC; Lilly, JM; (2016) A Widely Linear Complex Autoregressive Process of Order One. IEEE Transactions on Signal Processing , 64 (23) pp. 6200-6210. 10.1109/TSP.2016.2599503. Green open access

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Abstract

We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, extended to include a widely linear autoregressive term. This process can then capture elliptical, as opposed to circular, stochastic oscillations in a bivariate signal. The process is order one and is more parsimonious than alternative stochastic modeling approaches in the literature. We provide conditions for stationarity, and derive the form of the covariance and relation sequence of this model. We describe how parameter estimation can be efficiently performed both in the time and frequency domain. We demonstrate the practical utility of the process in capturing elliptical oscillations that are naturally present in seismic signals.

Type: Article
Title: A Widely Linear Complex Autoregressive Process of Order One
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TSP.2016.2599503
Publisher version: http://dx.doi.org/10.1109/TSP.2016.2599503
Language: English
Additional information: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Keywords: Seismic measurements, Time series analysis, autoregressive processes, parameter estimation, maximum likelihood estimation, spectral analysis
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/1494954
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