Abstract: Nonlinear chirplet transform, a new parametric method for time-frequency analysis was proposed by replacing the linear chirp kernel by a nonlinear polynomial kernel. By choosing the proper kernel characteristic parameters, the nonlinear chirplet transform can render a time frequency distribution of excellent concentration for signals whose instantaneous frequency trajectory is an arbitrary function of time. In this paper, the polynomial chirplet transform was applied to estimate the polynomial phase signals with arbitrary order. As the performance of the nonlinear chirplet transform highly depends on the kernel characteristic parameters, an algorithm to evaluate these parameters was developed in order to estimate the instantaneous frequency and the phase parameters of the polynomial phase signal. The effectiveness of the algorithm was validated by analyzing the signals from numerical simulation.

Key words: vibration and wave, polynomial phase signal, nonlinear chirplet transform, polynomial kernel function, time frequency analysis, instantaneous frequency estimation

摘要： 通过多项式非线性核函数取代线性调频小波变换中的线性核函数，提出一种新的参数化时频分析方法：非线性调频小波变换。对瞬时频率是时间任意连续函数的信号而言，选择合适的多项式核特征参数，非线性调频小波变换的时频分布有良好的时频聚集性。应用非线性调频小波变换分析任意阶次多项式相位信号。由于非线性调频小波变换的性能取决于多项式核特征参数，本文还给出非线性调频小波变换的核特征参数估计算法，进一步可实现多项式相位信号的瞬时频率和参量估计。仿真信号验证算法的有效性。

关键词: 振动与波, 多项式相位信号, 非线性调频小波变换, 多项式核函数, 时频分析, 瞬时频率估计