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APPLICATION OF PREDICTION METHODS TO NONLINEAR PERCUSSION INSTRUMENTS

机译:预测方法在非线性打击乐器中的应用

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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.
机译:由非线性打击乐器(如Cymbals和Gong)产生的大多数振动和声音都表现出混沌动力系统的典型特性。更具体地,对于大振幅的振动,非线性效应变为优势并且可以导致混沌行为。在分析和产生这种时间序列的角度下,必须参与最近的非线性信号处理的进步。作为光谱线性方法不能计算具有宽带傅里叶谱的时间序列,使用时间延迟坐标进行伪相空间的重建,并且计算重建动态的近似值,似乎自然地进行到伪相空间。已经使用基于重构相空间中的本地邻域与邻域演化建模的预测方法。从短时间学习时间序列允许从短学习时间序列产生长持续时间信号的算法。合成时间序列预计将呈现与原版相同的动态特性(分形维数和Lyapunov指数)。然后将该方法应用于从钹强制振荡的实验获得的实验时间序列,以及自由振荡的锣。

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