Chaotic signal processes and associated nonlinear filters

Robert C. McCarty

doi:10.1117/12.271126

4 April 1997 Chaotic signal processes and associated nonlinear filters

Robert C. McCarty

Proceedings Volume 3026, Nonlinear Image Processing VIII; (1997) https://doi.org/10.1117/12.271126
Event: Electronic Imaging '97, 1997, San Jose, CA, United States

Abstract

A chaotic signal process is generated by use of a continuous but nowhere differentiable Weierstrass function as a force function in Duffing's second-order nonlinear differential equation. In the particular cases where Duffing's equation represents the mechanical behavior of a simple pendulum where only the mass of the 'bob' changes in time, an analytical solution is obtained by the use of Hammerstein integrals. In the more-complicated case where the mass of the 'bob' and the length of the pendulum rod are both changing in time, the resulting solution is obtained numerically. In any detailed analysis of a chaotic signal process, nonlinear filters are used to determine the existence and nature of an attractor or repeller as discussed. By a simple change of parametric values in the Weierstrass function, other chaotic signal processes are easily generated.

Citation Download Citation

Robert C. McCarty "Chaotic signal processes and associated nonlinear filters", Proc. SPIE 3026, Nonlinear Image Processing VIII, (4 April 1997); https://doi.org/10.1117/12.271126

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