分数阶Fourier域多分量LFM信号间的分辨研究

Research on resolution among multi-component LFM signals in the fractional Fourier domain

在分数阶Fourier域内,当多分量线性调频(LFM)信号的初始频率和调频率相近时,信号的尖峰会出现无法分辨的现象,导致目标信号漏检.文中分析了LFM信号在分数阶Fourier域的频谱分布特征,以及离散分数阶Fourier变换计算条件下LFM信号的频谱分布特征.推导了两个LFM信号在分数阶Fourier域的临界分辨距离,以及两个LFM信号尖峰之间的距离与量纲归一化因子的变化关系,发现选择合理的量纲归一化因子可以增大两个信号尖峰之间的距离.文中提出一种量纲归一化因子优化选择的方法,该方法可以提高分数阶Fourier变换对多分量LFM信号的分辨能力.最后,仿真结果验证了该方法的有效性.

When the initial frequencies and chirp-rates of multi-component linear frequency modulation （LFM or chirp） signals are close, in the fractional Fourier domain （FRFD）, the phenomenon may occur that the peaks of multi-component LFM signals can＇t be distinguished. It results in some target signals undetected. In this paper, firstly, the spectrum distribution characteristics of a continuous LFM signal in FRFD are analyzed, and the spectrum distribution characteristics of a discrete LFM signal in the discrete FRFD are also analyzed. Secondly, the critical resolution distance between two LFM signals in the FRFD is deduced, and the relationship between dimensional normalization parameter and the distance between two LFM signals in the FRFD is also deduced. It is discovered that selecting a proper dimensional normalization parameter can increase the distance. Finally, a method to select the dimensional normalization parameter is proposed, which can improve the resolution ability of the FRFT for the multi-component LFM signals. And its effectiveness is verified by the simulation results.