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Research progress of the fractional Fourier transform in signal processing

查看全文 作  者:TAO [1]Ran;DENG [1,2]Bing;WANG [1]Yue 高影响力作者 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高影响力机构 出  处:《Science in China(Series F)》索引2006年第49卷第1期,共25页高影响力期刊 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 es-sentially 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 com-prehensively 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:信号处理 部分傅里叶变换 时频分析 通信理论
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