利用曲线拟合方法分析暂态振荡信号

提出了一种利用曲线拟含定量分析暂态振荡信号的方法.该方法给出的暂态振荡信号模型能够反映振荡的幅度和频率随时间变化的规律.提出了利用曲线拟合方法确定该摸型的具体参数的步骤:首先利用三次样条插值求出信号的上包络曲线,对其采用指数衰减信号模型来进行拟合以描述信号振荡幅度的变化参数;然后得到信号频率变化部分的正弦形式,利用 Hilbert 变换提取出正弦部分的相位,并采用幂指数信号模型进行拟合以描述信号振荡频率的变化参数.与以往分析暂态振荡信号的方法相比,该方法可对信号进行定量分析.仿真和试验结果表明,采用曲线拟合方法确定模型参数,实现过程简单,均方根误差小;对实际信号的分析则表明所提出的模型能够真实地反映出实际暂态振荡信号的变化规律.

Analysis of transient oscillatory signal by using curve fitting method

A quantitative analysis method was proposed by using the curve fitting to analyze transient oscillatory signal.The model of transient oscillatory signal given can reflect the rule that the oscillatory amplitude and frequency of signal varies with time.The parameters of the model were determinated by means of curve fitting.At first the upper envelope curve of the signal was derived by cubic spline interpolation and the derived envelope curve was fitted by exponential attenuation model,which can describe the varied parameter of the oscillatory amplitude of the signal.Then the phase of the derived sine form of varied frequency was extracted by Hilbert transform and the phase was fitted by power exponent model,which could describe the varied parameter of the oscillatory frequency of the signal.Compared with the previous analysis methods,the method presented can analyze transient oscillatory signal quantificationally.The simulation and experiment result confirm the correctness of determinating the parameter of the presented model by means of curve fitting.The analysis of actual signal shows that the presented model can factually reflect the varied rule of practical transient oscillatory signal.