一种新的分数阶傅立叶变换快速算法  

A Novel Fast Algorithm for Fractional Fourier Transform

作　　者：平先军[1] 陶然[1] 周思永[1] 王越[1] 

机构地区：[1]北京理工大学电子工程系,北京100081

出　　处：《电子学报》2001年第3期406-408,共3页Acta Electronica Sinica

基　　金：国家自然科学基金!(No .69972 0 0 3)

摘　　要：本文给出了分数阶傅立叶变换 (FRFT)的定义 ,介绍了已有的几种离散FRFT快速算法 ,并简要分析了这几种算法的优缺点 .在此基础上提出了一种新的FRFT快速算法 .该算法避开特征值与特征向量的匹配问题 ,具有易理解、易实现、效果好等优点 .并且在改变分数阶幂时不需重新计算整个过程 ,只需计算一个对角矩阵 .为与其他方法作比较 ,作者最后对几个典型信号作了计算机仿真 。The definition of the Fractional Fourier Transform (FRFT) has been presented in the paper.Several fast algorithms of discrete FRFT have been reviewed.The performances of these algorithms have been analyzed briefly.Based on this analysis,a new algorithm for efficient and accurate computation of FRFT is given.This algorithm needs not to consider the match between eigenvalues and eigenvectors.There are some advantages such as easily understanding and implementing with excellent effect.And if the rotational angle is changed,only a diagonal matrix should be recomputed.A few simulation results for some typical signals are provided to compare with previous ones by other methods in the end.

关 键 词：分数阶傅立叶变换 Hermite函数 时频分析 

分 类 号：O174.22[理学—数学]