基于分数阶傅里叶变换的chirp信号时频分析

提出了一种新的基于分数阶傅里叶变换的伪维格纳分布(PWD),用于单分量或多分量chirp信号的分析。首先通过搜索二阶分数阶傅里叶变换矩的极值点,寻找最佳变换域,然后利用旋转的短时傅里叶变换,在分数阶傅里叶变换域中实现各分量chirp信号间的分离,以抑制交叉项及噪声项的干扰。在已知信号模型的前提下,还给出了分数阶傅里叶变换最佳旋转角度的经验计算公式,以辅助信号分析。仿真实验表明,通过对时频平面的旋转,所提出的方法能够在分数阶傅里叶变换域中,很好地抑制多分量信号间的交叉项干扰,更好地提取信号的时频信息。

Chirp signal analysis based on PWD in fractional fourier transform domain

A new pseudo Wigner distribution (PWD) in the Fractional Fourier transform (FT) domain is proposed to analyze single or multi-component chirp signals. Rotated short-time Fourier transform (STFT) is used to realize the proposed distribution, and the appropriate fractional domain is found from the knowledge of the second-order fractional FT moments. By analyzing the signal in the most appropriate fractional domain, the proposed time-frequency distribution preserves the WD auto-terms and cancels the cross-terms when there are several signal components. The proposed method is easy to perform without significant additional computational cost. Simulation results prove its qualitative advantage in the time-frequency representation when the calculation is done in the optimal fractional domain.