分数阶傅里叶变换的数值实现

A Numerical Algorithms of Fractional Fourier Transform

信号及其傅里叶变换可以分别反映信号在时频两域内的信息。傅里叶变换是一种常用的数学工具 ,在数学、物理及工程技术领域都得到了十分广泛的应用。介绍了一种崭新的信号分析工具———分数阶傅里叶变换 ,并用经典的傅里叶变换的观点对分数阶傅里叶变换进行了解释。对于分数阶傅里叶变换的实现 ,因一般情况下分数阶傅里叶变换给不出解析表达式 ,故分数阶傅里叶变换的数值算法的研究是十分重要的。给出了分数阶傅里叶变换的较准确的数值计算方法。

Signal and it's Fourier transform can reflect the info of time domain and frequence domain independently. As a usually math tool, Fourier transform is using in math, physical and engineering field widely. A new tool for signal analysis,which is named Fractional Fourier transform(FRFT), is introduced. It is interpreted in view of the classic Fourier transform. It is important to study the numerical algorithms of FRFT, because usually the FRFT can not be given to a analytical expression. A numerical algorithms of FRFT is given. It is possible to separate the distortion from the simple Gaussian signal on which a chirp distortion has been superimposed by using fractional transform.