基于改进的Wigner-Ville分布与Chirp-Z变换的高分辨时频分析方法
High-Resolution Time-Frequency Analysis Based on Improved Wigner-Ville Distribution with Chirp-Z Transformation

以Wigner-Ville分布(WVD)为代表的二次非线性时频分析方法具有良好的时频聚焦性，适合用于非平稳信号的时频分析，但在处理复杂多分量信号时，会产生严重的交叉干扰项影响人们对信号频谱的分析判断。伪Wigner-Ville分布(PWVD)和平滑伪Wigner-Ville分布(SPWVD)在WVD的基础上加窗改进核函数，可以有效抑制交叉项干扰，但也会降低对信号的时频分辨率。本文使用Chirp-Z变换(CZT)替换PWVD和SPWVD中的快速傅里叶变换(FFT)，得到两种高分辨时频分析方法PWVD-CZT和SPWVD-CZT，通过数值实验验证两种方法均可有效提高对信号的时频分辨率，SPWVD-CZT处理主频低、频带窄的复杂多分量非平稳信号具有更大的优势。
The quadratic nonlinear time-frequency analysis method represented by the Wigner-Ville distribution (WVD) has good time-frequency focusing and is suitable for the time-frequency analysis of non-smooth signals, but when dealing with the complex multi-component signals, it will produce serious cross-interference terms affecting people’s analytical judgment of the signal spectrum. Pseudo Wigner-Ville distribution (PWVD) and smoothed pseudo Wigner-Ville distribution (SPWVD) improve the kernel function by adding a window on top of WVD, which can effectively suppress the cross term interference, but also reduce the time-frequency resolution of the signal. In this paper, the Chirp-Z transform (CZT) is used to replace the fast Fourier transform (FFT) in PWVD and SPWVD to obtain two high-resolution time-frequency analysis methods, PWVD-CZT and SPWVD-CZT, and it is verified through numerical experiments that the two methods are effective in improving the time-frequency resolution of the signal, and SPWVD-CZT has a greater advantage in dealing with the complex multi-component non-stationary signals with low primary frequency and narrow frequency band. The SPWVD-CZT has more advantages in dealing with complex multi-component non-stationary signals with low primary frequency and narrow frequency bands.