Most of the vibrations and sounds produced by nonlinear percussion instruments, such as cymbals and gongs, exhibit the typical properties of chaotic dynamical systems. More specifically, for large amplitude of vibrations, nonlinear effects becomes preponderant and can lead to chaotic behaviour. In the perspective of analyzing and generating such time series, advantage must be taken of the recent advances in non-linear signal processing. As spectral linear methods are not able to compute time series having broadband Fourier spectra, it seems natural to proceed to the reconstruction of a pseudo-phase space, using time-delayed coordinates, and to compute an approximation of the reconstructed dynamics. A prediction method based on the modeling of the local neighbourhood-to-neighbourhood evolution in the reconstructed phase space has been used. An algorithm which allows, from a short learning time series, to generate long duration signals, has been written. The synthetic time series are expected to present the same dynamical properties (fractal dimension and Lyapunov exponents) as the original. The method is then applied to experimental time series obtained from experiments on forced oscillations of a cymbal, and a freely oscillating gong.
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