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.