  The non-stationary dynamics of a bouncing ball, comprising of both periodic
as well as chaotic behavior, is studied through wavelet transform. The
multi-scale characterization of the time series displays clear signature of
self-similarity, complex scaling behavior and periodicity. Self-similar
behavior is quantified by the generalized Hurst exponent, obtained through both
wavelet based multi-fractal detrended fluctuation analysis and Fourier methods.
The scale dependent variable window size of the wavelets aptly captures both
the transients and non-stationary periodic behavior, including the phase
synchronization of different modes. The optimal time-frequency localization of
the continuous Morlet wavelet is found to delineate the scales corresponding to
neutral turbulence, viscous dissipation regions and different time varying
periodic modulations.
