Article ID Journal Published Year Pages File Type
1897263 Physica D: Nonlinear Phenomena 2008 11 Pages PDF
Abstract

Recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems, denoising, as well as detection of deterministic signals embedded in noise. Though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise. Computations using examples from harmonic processes, autoregressive models, and outputs from nonlinear systems are shown to illustrate this relationship. Finally, the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test. Results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub-optimal when compared to well-known detectors based on the likelihood ratio.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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