Research progress of the fractional Fourier transform in signal processing  

作　　者：TAO Ran DENG Bing WANG Yue 

机构地区：[1]Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China [2]Department of Electronic Engineering, Naval Aeronautical Engineering Institute, Yantai 264001, China

出　　处：《Science in China(Series F)》2006年第1期1-25,共25页中国科学（F辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.60232010 and 60572094);the Teaching and Research Award for 0utstanding Young Teachers in Higher Education Institutions of M0E,P.R.C.;the Ministerial Foundation of China(Grant No.6140445).

摘　　要：The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.

关 键 词：fractional Fourier transform signal processing time-frequency analysis. 

分 类 号：TN911.7[电子电信—通信与信息系统]