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针对低信噪比下线性调频信号的检测问题,提出了一种简明分数阶傅里叶变换方法。该变换借助chirp相乘和傅里叶变换对时频平面上的频率轴进行旋转,以获取信号在各个角度下频率轴上的频谱分布。对时频分布呈直线状的线性调频信号,简明分数阶傅里叶变换能在特定角度上将信号能量聚集成尖锐的强能量峰,从而提高信噪比,实现对线性调频信号的可靠检测和参数估计。数值仿真和实验验证结果表明,简明分数阶傅里叶变换可对较低信噪比的线性调频信号实现有效检测,并由变换域峰值的位置对信号参数进行准确估计。相比于传统的分数阶傅里叶变换方法,简明分数阶傅里叶变换的复杂度更低,离散计算效率更高,在对噪声掩盖下的线性调频信号进行检测和参数估计时能更好地满足实时处理的要求。
Aiming at the problem of LFM signal detection at low SNR, a simple fractional Fourier transform method is proposed. The transform rotates the frequency axis on the time-frequency plane by means of chirp multiplication and Fourier transform to obtain the spectral distribution of the signal on the frequency axis at various angles. For linear chirp signals with linear time-frequency distribution, concise Fractional Fourier Transform can gather signal energy into sharp strong energy peak at a specific angle so as to improve signal-to-noise ratio and achieve reliable detection of linear frequency modulated signals Parameter Estimation. The numerical simulation and experimental results show that the concise fractional Fourier transform can effectively detect LFM signals with lower signal-to-noise ratio, and the signal parameters can be accurately estimated from the peak position of the transform domain. Comparing with the traditional Fractional Fourier Transform method, the concise Fractional Fourier Transform has lower complexity and discrete computation efficiency, which can be better when detecting and parameter estimating the chirp signal covered by noise Meet real-time processing requirements.