基于分数阶傅里叶变换的线性调频信号的自适应时频滤波

AN ADAPTIVE TIME-FREQUENCY FILTERING METHOD BASED ON FRACTIONAL FOURIER TRANSFORM FOR LINEAR FREQUENCY MODULATION SIGNALS

本文提出了一种基于分数阶傅里叶变换的线性调频 (LFM )信号的自适应滤波方法 ,利用该变换等同于对信号在时频平面进行旋转这一重要特性 ,将混迭有噪声的信号以特定的旋转角作分数阶傅里叶变换 ,使得信号与噪声在变换域中的交迭达到最小 ;在此基础上 ,通过窄带通滤波器对LFM信号进行抽取 ,去除大部分的噪声能量 ,然后 ,再经过分数阶傅里叶反变换 ,恢复出原来的LFM信号。理论分析和仿真表明 ,该方法不仅可获得明显的信噪比的改善 ,而且具有算法简单及信号失真小等特点 ,和其它基于二维时频分析工具的滤波算法相比 ,降低了计算的复杂度 ,其实现更为简便。

The aim of this paper is to propose an adaptive method for filtering the linear FM signal embedded in white Gaussian noise. The idea that the fractional Fourier transform (FRFT) for a signal is equivalent to rotating the signal on time-frequency plane is used. First, a noisy LFM signal rotated to a certain angle by the FRFT will result in the least spectrum overlap between the signal and noise in fractional Fourier domain. Then, on the basis of dechirping the LFM signal ,a narrowband filter is exploited to extract the signal and depress most of the noise energy. Finally, the denoised LFM signal is rotated back to the time domain using an inverse FRFT. Performance of the proposed method is seen through its simplicity in computation and in their improvement SNR. Some theoretical analysis and simulation results are included to demonstrate the validity of the method and the results have shown that remarkable improvement of SNR and tolerable signal distortion are obtained. In addition, when compared with other two-dimension time-frequency filtering algorithms, it is seen to be easy in computation and simple in implementation.