用于计算离散分数阶傅里叶变换的MA-CDFRFT算法改进  

The modification of MA-CDFRFT algorithm used in computing discrete fractional Fourier transform

作　　者：陈鹏[1] 侯朝焕[2] 马晓川[2] 

机构地区：[1]中国科学院研究生院,北京100049 [2]中国科学院声学研究所,北京100080

出　　处：《中国科学院研究生院学报》2007年第2期229-234,共6页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：国家自然科学基金项目(60472101)资助

摘　　要：基于中心类型DFT矩阵特征分解的MA-CDFRFT(Multiangle Centered Discrete Fractional Fourier Transform)算法在计算一组离散分数阶傅里叶变换DFRFT(Discrete Fractional Fourier Transform)时充分利用FFT运算来减小运算量.结合偶数点离散傅里叶变换DFT(Discrete Fourier Transform)运算的对称性原理,通过数学推导将MA-CDFRFT算法中的一维对称性扩展到频率和变换阶数的二维平面上.利用这个二维对称性原理,改进算法将原算法的主要计算量减小了一半左右.仿真测试结果证明了改进算法的正确性.The MA-CDFRFT（Multiangle Centered Discrete Fractional Fourier Transform） algorithm which is based on the eigendecomposition of the centered version DFT matrix makes full use of the FFT operation to reduce the computations in computing a group of DFRFT operations. Combining the symmetry principle of DFT （Discrete Fractional Fourier Transform） operation with even numbers, expands the one-dimensional symmetry principle in MA- CDFRFT algorithm to the two-dimensional plane of frequency and transform the order according to the mathematical derivation. Utilizing this two-dimensional symmetry principle, the modified algorithm decreases the computations of the original algorithm to approximately one half. And the simulation test proves the correctness of the modified algorithm.

关 键 词：离散分数阶傅里叶变换 离散傅里叶变换 多角度中心型离散分数阶傅里叶变换 快 速傅里叶变换 

分 类 号：TN911.72[电子电信—通信与信息系统]