Sampling and sampling rate conversion of band limited signals in the fractional Fourier transform domain

被引：105

作者：

Tao, Ran ^{[1
]}

Deng, Bing ^{[1
,2
]}

Zhang, Wei-Qiang ^{[3
]}

Wang, Yue ^{[1
]}

机构：

[1] Beijing Inst Technol, Dept Elect Engn, Beijing 100081, Peoples R China

[2] Naval Aeronaut Engn Inst, Dept Elect Engn, Yantai 264001, Peoples R China

[3] Tsing Hua Univ, Dept Elect Engn, Beijing 100084, Peoples R China

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2008年 / 56卷 / 01期

基金：

中国国家自然科学基金;

关键词：

fractional Fourier transform (FRFT); sampling rate conversion; sampling theorem;

D O I：

10.1109/TSP.2007.901666

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) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations.

引用

页码：158 / 171

页数：14

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