Analysis and comparison of discrete fractional fourier transforms

被引：48
作者：
Su, Xinhua [1 ,2 ]
Tao, Ran [1 ,2 ]
Kang, Xuejing [3 ]
机构：
[1] Beijing Inst Technol, Sch Informat & Elect, Beijing, Peoples R China
[2] Beijing Key Lab Fract Signals & Syst, Beijing 100081, Peoples R China
[3] Beijing Univ Posts & Telecommun, Inst Sensing Technol & Business, Beijing 100876, Peoples R China
来源：
SIGNAL PROCESSING | 2019年 / 160卷
基金：
中国国家自然科学基金;
关键词：
Fractional fourier transform; Linear canonical transform; Eigenvector decomposition; Commuting matrices; OPTIMAL ORTHONORMAL EIGENVECTORS; GAUSSIAN-LIKE EIGENVECTORS; DIGITAL COMPUTATION; FAST ALGORITHMS; MATRIX; DISCRETIZATION; DECOMPOSITION; DOMAINS;
D O I：
10.1016/j.sigpro.2019.01.019
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
The fractional Fourier transform (FRFT) is a powerful tool for time-varying signal analysis. There exist various discrete fractional Fourier transforms (DFRFTs); in this paper, we systematically analyze and compare the main DFRFT types: sampling-type DFRFTs and eigenvector decomposition-type DFRFTs. First, for the existing sampling-type DFRFTs, we perform concrete analyses and comparisons of their applicable conditions and then establish their equivalence relationship. Then, for various eigenvector decomposition-type DFRFTs, their common mechanisms are extracted and thus they are effectively classified. In addition, as the extended version of DFRFTs, discrete counterparts of the linear canonical transform (LCT) and simplified FRET (SFRFT) are summarized and classified. Our work is instructive for research about the choice of a more appropriate DFRFT in different applications, which is also supported by simulation experiments. Finally, for the DFRFT, DLCT and DSFRFT, two applications regarding detection for chirp signals and optical imaging are investigated to intuitively analyze their differences. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：284 / 298
页数：15
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