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Model-based detector and extraction of weak signal frequencies from chaotic data. (English) Zbl 1306.37093

Summary: Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (Hénon map, chaotic circuit, and NH\(_3\) laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector. Particularly, the signal frequencies can be extracted accurately in the time-frequency space. By comparing the model-based method with the standard denoising wavelet technique as well as supervised principal components analysis detector, we further show that the nonlinear dynamics and neural network-based approach performs better in extracting frequencies of weak signals hidden in chaotic time series.{
©2008 American Institute of Physics}

MSC:

37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
34C28 Complex behavior and chaotic systems of ordinary differential equations

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References:

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