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

2010/03/03 by Benjamin Ricaud, Françoise Briolle, Francoise Briolle +4
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #nlin.CD

paper · pdf · doi:10.48550/arxiv.1003.0734

openalex publication_date 2010/03/03 · arxiv created 2010/05/31 · arxiv updated 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Identification of fast-changing signals by means of adaptive chaotic transformations
• Chaotic time series Part I: Estimation of invariant properies in state space
• Chaotic time series Part II: System identification and prediction
• Using the Magnitude-Squared Coherence for Determining Order-Chaos Transition in a System Governed by Logistic Equation Dynamics
• The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet\n Transform