基于FRFT的线性调频信号欠采样快速检测方法

采用分数阶Fourier变换对线性调频信号(Linear Frequency Modulation,LFM)进行检测与参数估计时,由于信号的特征未知,需要运用二维搜索方法确定分数阶Fourier变换的最佳旋转角度.该方法运算量巨大.为减少运算量,本文推导了欠采样前后LFM信号的分数阶Fourier变换最佳能量聚集旋转角度关系,证明了无噪LFM信号的调频率估计可以完全不受Nyquist采样定理的限制;通过推导分析欠采样含噪LFM信号在最佳分数阶Fourier域的信噪比,给出了欠采样倍数M对LFM信号检测的影响及其选取原则;最终提出一种基于欠采样理论的LFM信号快速检测方法.实验结果表明,当M选取合适时,利用原始信号的欠采样样本即可对LFM信号实现有效检测,快速确定其调频率.

Fast Detection of LFM Signal Based on FRFT and Sub-Nyquist Sampling

The relationship between the optimal rotation angle of fractional Fourier transform(FRFT)of the undersampled signal and that of the original signal was studied.It was proved that the chirp-rate of noiseless linear frequency modulation(LFM)signal can be estimated correctly even though the signal was undersampled.By deducing and analyzing the signal to noise ratio(SNR)in the optimal fractional Fourier domain,the impact of subsampling rate on detection of LFM signal was discussed.Finally,a novel method was proposed to realize fast detection of LFM signal.Simulation results show that when the subsampling rate is set properly,the detection and parameter estimation of LFM signal can be realized rapidly by applying FRFT to the undersampled signal.