Digital computation of the weighted-type fractional Fourier transform

查看全文 作　　者：MEI [1,2]Lin;ZHANG [1]QinYu;SHA [2]XueJun;ZHANG [1,2]NaiTong

机构地区：[1]Shenzhen Graduate School, Harbin Institute of Technology;[2]Communication Research Center, Harbin Institute of Technology

出　　处：《Science China(Information Sciences)》索引2013年第56卷第7期,共12页

基　　金：supported in part by National Natural Science Foundation of China (Grant No. 61201146);National Basic Research Program of China (973 Program) (Grant No. 2009CB320402) 摘　　要：The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy Δt = T/N = 1/N(1/2) when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. 关键词：分数傅里叶变换数字计算加权傅立叶变换算法 WDFT 采样周期离散算法特征值分解

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Digital computation of the weighted-type fractional Fourier transform

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