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A Widely Linear Complex Autoregressive Process of Order One

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A Widely Linear Complex Autoregressive Process of Order One. / Sykulski, Adam M.; Olhede, Sofia C.; Lilly, Jonathan M.
In: IEEE Transactions on Signal Processing, Vol. 64, No. 23, 7539658, 01.12.2016, p. 6200-6210.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Sykulski, AM, Olhede, SC & Lilly, JM 2016, 'A Widely Linear Complex Autoregressive Process of Order One', IEEE Transactions on Signal Processing, vol. 64, no. 23, 7539658, pp. 6200-6210. https://doi.org/10.1109/TSP.2016.2599503

APA

Sykulski, A. M., Olhede, S. C., & Lilly, J. M. (2016). A Widely Linear Complex Autoregressive Process of Order One. IEEE Transactions on Signal Processing, 64(23), 6200-6210. Article 7539658. https://doi.org/10.1109/TSP.2016.2599503

Vancouver

Sykulski AM, Olhede SC, Lilly JM. A Widely Linear Complex Autoregressive Process of Order One. IEEE Transactions on Signal Processing. 2016 Dec 1;64(23):6200-6210. 7539658. Epub 2016 Aug 10. doi: 10.1109/TSP.2016.2599503

Author

Sykulski, Adam M. ; Olhede, Sofia C. ; Lilly, Jonathan M. / A Widely Linear Complex Autoregressive Process of Order One. In: IEEE Transactions on Signal Processing. 2016 ; Vol. 64, No. 23. pp. 6200-6210.

Bibtex

@article{e0443ff6796c41e29f2003405718aec5,
title = "A Widely Linear Complex Autoregressive Process of Order One",
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.",
keywords = "autoregressive processes, maximum likelihood estimation, parameter estimation, seismic measurements, spectral analysis, Time series analysis",
author = "Sykulski, {Adam M.} and Olhede, {Sofia C.} and Lilly, {Jonathan M.}",
year = "2016",
month = dec,
day = "1",
doi = "10.1109/TSP.2016.2599503",
language = "English",
volume = "64",
pages = "6200--6210",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "23",

}

RIS

TY - JOUR

T1 - A Widely Linear Complex Autoregressive Process of Order One

AU - Sykulski, Adam M.

AU - Olhede, Sofia C.

AU - Lilly, Jonathan M.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - autoregressive processes

KW - maximum likelihood estimation

KW - parameter estimation

KW - seismic measurements

KW - spectral analysis

KW - Time series analysis

U2 - 10.1109/TSP.2016.2599503

DO - 10.1109/TSP.2016.2599503

M3 - Journal article

AN - SCOPUS:84994472534

VL - 64

SP - 6200

EP - 6210

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 23

M1 - 7539658

ER -