基于短时分数阶傅里叶变换的瞬时频率估计误差分析

Error Analysis of Instantaneous Frequency Estimation Based on Short-time Fractional Fourier Transform

信号的瞬时频率估计作为雷达信号处理的一项重要内容,对于目标的检测和识别起着重要作用。利用短时分数阶傅里叶变换具有更好时频分辨力的特点,分析了利用短时分数阶傅里叶变换对三次相位非线性调频信号进行瞬时频率估计的精度与窗函数、窗长间的关系。结果表明:当采用高斯窗时能够获得最高估计精度,且最佳窗长L与时宽和带宽积σ_tσ_f和信号调频率变化率k满足L=(3σ_tσ_f/2k)^(1/3).通过仿真实验验证了结论。

As an important content on radar signal processing,instantaneous frequency estimation plays an essential role in target detection and recognition. The higher time-frequency resolution of short-time fractional Fourier transform（ STFRFT） is used to analyze the relationship among window function,window width and the instantaneous frequency estimation precision of cubic phase non-LFM signal. The result shows that,when Gauss window is used,the estimation precision is the highest; the prime window width L,the product of pulse width and band width σ_tσ_f and the frequency fluctuation rate k should meet L=（3σ_tσ_f/2k）^（1/3）. Finally,the result is verified through simulation.