Study on Singularity of Chaotic Signal Based on Wavelet Transform

Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.