Analysis and separation of time-frequency components in signals with chaotic behavior

Benjamin Ricaud; Francoise Briolle; F. Clairet

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arXiv · 1003.0734

Analysis and separation of time-frequency components in signals with chaotic behavior

Benjamin Ricaud·Francoise Briolle·F. Clairet

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Abstract

The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic chirps. The linear chirp transformation is able to discriminate and extract particular chaotic components in non-stationary square integrable signals. This is demonstrated in an example studying the reflectometry measures of a turbulent plasma. The hyperbolic chirp transformation is designed for the detection and extraction of chaotic parts in self-similar processes such as stochastic motions. Mathematical connections are made between these two methods and other well-known transformations.

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Benjamin Ricaud, Francoise Briolle, F. Clairet. 2010-05-31. Analysis and separation of time-frequency components in signals with chaotic behavior. https://arxiv.org/abs/1003.0734

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