Abstract
Owing to the limitations of the concept of frequency for power spectrum and the inherent defects of Fourier transform, a novel concept of general local frequency is proposed. Based on a approach to adaptive peak decomposition, the dynamic feature in frequency domain varying with parameter r of Duffing system driven by periodic signal is investigated. And a phenomenon of frequency bifurcation is found. Moreover, coninuous frequency bands exist near the central frequency of chaos time seriers at different values of parameter r and their shapes are similar. By demodulation analysis of Hilbert transform, the modulation characteristic and modulation similarity of chaos time seriers are summarized. The above study shows that the proposed approach to general local frequency based on adaptive peak is effective for freature extraction in frequency domain of Duffing system. It provides a new method to observe a continunous distribution of frequency bands for the non-linear system in chaotic state.
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