离散分数阶Fourier变换的阶数分解算法  

Discrete fractional Fourier transform algorithm via fractional domain decomposition

作　　者：谢为群[1] 刘中杰[1] 马世伟[1] 

机构地区：[1]上海大学机电工程与自动化学院上海市电站自动化技术重点实验室,上海200072

出　　处：《电子测量技术》2009年第2期63-65,104,共4页Electronic Measurement Technology

摘　　要：分数阶Fourier变换在科学计算和工程中有广泛应用前景,但现有的离散分数阶Fourier变换(DFRFT)缺乏有效的快速算法。本文给出了一种采用阶数分解的DFRFT算法,由特定阶数DFRFT的加权和可得到任意分数阶域的DFRFT,权系数由DFTHermite本征值和附加零构成序列的离散Fourier反变换(IDFT)得到,且在搜索最佳分数阶域的过程中仅需计算一次IDFT,无需重新计算其所有变换核,从而可有效减少运算量,适合于应用在分数阶域的多分量信号检测和滤波处理中,仿真结果表明了该算法的有效性。Fractional Fourier Transform can be widely used in scientific calculation and engineering. However it lacks fast algorithms for discrete Fractional Fourier Transform （DFRFT）. In this paper,a DFRFT algorithm using fractional domain decomposition is proposed. With this method, the DFRFT at any fractional domain of a signal can be obtained by a weighted combination of its DFRFTs at special fractional domains, the weighting coefficients are obtained from an inverse Discrete Fourier Transform（ IDFT） computation of a series consisted of DFT Hermite eigen values and appended zeros. In searching optimal fractional domain,it doesn＇t to calculate all of the transform kernels and just need to do an IDFT computation once. Hence, the computational burdens can be reduced efficiently. It can be used for multicomponent signal detection and filtering in fractional Fourier domains. Numerical simulation results manifested the effectiveness of this method.

关 键 词：分数阶FOURIER变换 离散分数阶Fourier变换 阶数分解 

分 类 号：TN911.7[电子电信—通信与信息系统]