线性调频分数傅立叶变换理论及应用

基于普通傅立叶变换(FT)的特征函数,本文给出了一种连续时间信号的线性调频分数傅立叶变换(CFRFT)的表达方式,在此基础上,分析了CFRFT包括时移特性、展缩特性、反褶特性、时域微分特性、分数域频移特性、时域斜变信号相乘特性和Parseva l定理等变换性质,得出一些常用连续时间信号的CFRFT的变换表达式,说明了傅立叶变换可视为分数傅立叶变换(FRFT)的一个特例,对应用分数傅立叶变换分析系统具有启发作用。作为分数傅立叶变换的应用,解决了傅立叶变换不能有效分析时变系统的问题。

The Chirp-type Fractional Fourier Transform Theory and Applications

Based on the eigenfunctions of the ordinary Fourier transform(FT),this paper presents a definition of the chirp-type fractional Fourier transform(CFRFT) for continuous time signals.Some properties of CFRFT and the expressions for some common used signals are also given,which provides some implications for applying CFRFT.It is pointed out in this paper that the fractional Fourier transform(FRFT) is an extension of FT and FT is a special case of FRFT.To illustrate the application of FRFT,a swept frequency system and optimal filtering are also introduced,which can't be analyzed effectively with FT because of time varying systems involved.