Chaos in the APFM nonlinear adaptive filter

Authors:
Mohammad Saleh Tavazoei;Mohammad Haeri
Affiliations:
Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran;Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
Venue:
Signal Processing
Year:
2009

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Abstract

In this paper, we show that an amplitude phase frequency model (APFM) which is used as a nonlinear adaptive filter in signal processing can exhibit chaotic behavior. It is illustrated that both frequency and amplitude of the input components have effect on the filter characteristics which can lead the filter to behave chaotically for some values of these parameters. We have exploited different measures such as the Lyapunov exponents, bifurcation diagram, sensitivity to initial condition, and 0-1 test on time series to confirm our claim. Existence of the chaotic behavior in APFM does not conform to the prior conjectures about this filter.