关于线性调频信号滤波器设计仿真

Design on Linear Frequency Modulation Signal Filter Based on FRFT

针对含有噪声的线性调频信号(LFM)的滤波问题,因传统滤波方法仅能掌握信号在时域或者频域的全局特性,对线性调频信号这种非平稳信号滤波效果不理想。利用分数阶傅里叶变换(FRFT)对含有噪声的线性调频信号(LFM)进行滤波处理,对含有噪声信号进行FRFT,形成二维时频平面,由于LFM信号不同阶FRFT域有不同的能量聚集特性,通过扫描二维时频平面搜索峰值的最优阶,对信号进行最优阶的FRFT,在最优阶FRFT内设计带通滤波器,以峰值为中心对信号尖峰遮隔处理,选择带宽保留多数有用信号。再进行相同阶次反变换,得到滤除噪声后的信号。通过MATLAB建立模型对方法进行验证,仿真结果表明,分数阶傅里叶变换(FRFT)法能够达到优于传统时域和频域的理想滤波效果。

Because the traditional filtering methods can only grasp the global of signals in time domain or frequency domain,the filtering effect of non-stationary signal like linear frequency modulation is not ideal.For the filtering problem of linear frequency modulation signal(LFM)with noise,we applied the filtering process to the linear frequency modulation signal(LFM)using fractional Fourier transform(FRFT).The fractional Fourier transform was carried out to the signal with noise to form the two-dimensional time-frequency plane.Because LFM signal has different energy accumulation characteristics corresponding to different order fractional Fourier domains,the best order FRFT was taken to the signal through scanning two-dimensional time-frequency plane to search the best order of the peak value.Carry out bandpass filter design in the best order FRFT,process the mask to signal peak regarding the peak as the center and keep most useful signal when choosing bandwidth.Then take the some order inverse transform to get the signal witch has already filtered noise.Set up the model in MATLAB to verify the method.the simulation results show that fractional Fourier transform(FRFT)method can obtain the ideal filter effect which cannot be acquired by using the traditional time and frequency domain.