Digital computation of the weighted-type fractional Fourier transform

被引：0
|
作者：
MEI Lin [1 ,2 ]
ZHANG QinYu [1 ]
SHA XueJun [2 ]
ZHANG NaiTong [1 ,2 ]
机构：
[1] Shenzhen Graduate School, Harbin Institute of Technology
[2] Communication Research Center, Harbin Institute of Technology
来源：
Science China(Information Sciences) | 2013年 / 56卷 / 07期
基金：
中国国家自然科学基金;
关键词：
fractional Fourier transform (FRFT); weighted-type fractional Fourier transform (WFRFT); chirp- type fractional Fourier transform (CFRFT); discrete fractional Fourier transform; discrete Fourier transform (DFT);
D O I：
暂无
中图分类号：
TN911.7 [信号处理];
学科分类号：
0711 ; 080401 ; 080402 ;
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.
引用
收藏
页码：85 / 96
页数：12
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