关键词: 频响曲线, 瞬时幅值, 瞬时频率, 信号分解, 希尔伯特变换

Abstract:

：As one of the important tools in the realm of signal processing, the method of Hilbert transform is modified and it is used in applications to signal decomposition and nonlinear vibration analysis. Due to the characteristic of multi-harmonic component, the instantaneous amplitude and instantaneous frequency of the mechanical signal is decomposed to a slow varying oscillating and a rapidly varying oscillating by a low-pass filtering, and then the largest component of signal is obtained. After several iterations for the Hilbert transform, all the harmonic components of vibration signal are extracted. Then, the nonlinear vibration equations can be transformed to the standard equation with the instantaneous parameters, which are the function of instantaneous amplitude. The amplitude-frequency curve of response of system is obtained. With several numerical simulations, the effectiveness of the Hilbert transform is verified for the application to nonlinear analysis.

Key words: amplitude frequency curve, instantaneous amplitude, instantaneous frequency, signal decomposition, Hilbert transform