变分数阶傅氏变换及在时频建模中的应用

Variable Angle Fractional Fourier Transform and Its Application in Modeling the Signal's Time-Frequency Structure

主要讨论了一种将加紧支撑窗与分数阶傅里叶变换相结合的信号处理方法 .其原理在于将信号以短时窗函数截取 ,再配合分数阶傅里叶变换 .通过改变这种变换中的角度参量可以找出最大值 ,其最大值所对应的角度参量实际上就是在窗函数支撑内平均调频系数的直接反映 ,从而可以将具有不同调频系数的信号突出并加以提取 .利用这种方法可以获得信号的时频分布的基本“骨架” .这种方法基于对信号的线性变换 ,没有交叉项的影响 .通过合理的控制阈值及局部再加窗 ,对于具有多项式相位信号的时变频率建模有良好效果 .最后文章对一些影响因素进行了分析 .

A new method that uses the tight support window signal together with the fractional Fourier transform (FRFT) is discussed. The main idea is to multiply the signal for analysis with the tight support window signal and apply the FRFT to the result. By adjusting the angle parameter the max value can be searched out. The angle corresponding to the max value is actually a direct reflection of the average FM coefficient in the support of the window signal. By this way, the components that have different FM coefficient in the signal for analysis can be made even clearer and ready for extraction. This method is helpful in obtaining the basic framework of signals. The method is based on the linear transform and there is no effect on the mutual component. With some other techniques such as controlling the threshold properly and adding special window locally, perfect result in analyzing the signals with a polynomial phase can be obtained. Some factors that might worsen the result are discussed.