Abhinna Kumar Behera, A. N. Sekar Iyengar, Prasanta K. Panigrahi1
The non-stationary dynamics of a bouncing ball comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multiscale characterization of the time series discloses clear signature of self-similarity and periodicity. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to different periodic modulations. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multifractal detrended fluctuation analysis and Fourier methods. The discrete Daubechies basis set has been applied for detrending the temporal behavior to reveal the multifractal character underlying the dynamics.
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http://arxiv.org/abs/1304.6311
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