Chaotic signals and physical systems
- 1 January 1992
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 4 (15206149) , 113-116 vol.4
- https://doi.org/10.1109/icassp.1992.226473
Abstract
The methods for establishing a phase space or state space for a physical system from measurements of a scalar time series are reviewed, and the implications for the analysis of signals of the geometry of strange attractors are discussed. Classifying the physical systems by invariants on the attractor is seen to be the analog of classifying linear systems by the resonant response frequencies. The statistical properties of deterministic systems are used to perform this classifying. Methods for separating a chaotic signal of interest from contamination such as high dimensional noise are discussed. An example of a signal from a nonlinear circuit whose equations of evolution are unknown is discussed in detail and all the items mentioned are illustrated.<>Keywords
This publication has 11 references indexed in Scilit:
- Modeling chaotic systems with hidden Markov modelsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1992
- Modeling of chaotic time series for prediction, interpolation, and smoothingPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1992
- Noise reduction in chaotic time series using scaled probabilistic methodsJournal of Nonlinear Science, 1991
- Synchronizing chaotic circuitsIEEE Transactions on Circuits and Systems, 1991
- Computing the Lyapunov spectrum of a dynamical system from an observed time seriesPhysical Review A, 1991
- Optimal shadowing and noise reductionPhysica D: Nonlinear Phenomena, 1991
- A noise reduction method for chaotic systemsPhysics Letters A, 1990
- Information and entropy in strange attractorsIEEE Transactions on Information Theory, 1989
- Independent coordinates for strange attractors from mutual informationPhysical Review A, 1986
- Ergodic theory of chaos and strange attractorsReviews of Modern Physics, 1985