基于多尺度Chirplet稀疏分解和Wigner-Ville变换的时频分析方法

Time-frequency Analysis Method Based on Multi-scale Chirplet Sparse Decomposition and Wigner-Ville Transform

针对多分量多项式相位信号(mc-PPS)的Wigner-Ville分布存在的时频干扰问题,该文提出一种基于多尺度Chirplet稀疏分解和Wigner-Ville变换的时频分析方法。该方法采用多尺度的Chirplet基函数对信号进行投影分解,通过延时相关解调的分数阶傅里叶变换(FRFT)搜索投影系数最大的基函数,将搜索得到的基函数通过Wigner-Ville变换和最佳路径连接方法,逐次获得使分解信号能量最大的信号分量及其时频分布。仿真结果表明,该方法能在低信噪比条件下有效抑制等振幅mc-PPS的自交叉项和互交叉项的干扰,具有最佳的时频聚集性,克服了全局搜索基函数计算量大的问题,适用于非平稳信号的分析和处理。

To solve the problem of time-frequency interference existing in the multicomponent Polynomial Phase Signal （mc-PPS） Wigner-Ville distribution, a new time-frequency analysis method based on the multi-scaie Chirplet sparse decomposition and Wigner-Ville transform is proposed. This method projects mc-PPS onto the multi-scale Chirplet base functions, searching best base functions by the improved FRactional Fourier Transform （FRFT）. Through the Wigner-Ville transform and best path pursuit algorithm, the base functions constitute largest energy signals component and power distribution in turns. Simulation results verify that the proposed method can restrain effectively the cross-interference of constant mc-PPS in low Signal-to-Noise Ratio condition, maintain a high time-frequency aggregation, and overcome the large computation of global searching algorithm. Furthermore, this method is suitable for non-stationary signals analysis and processing.