Convolution theorems for the linear canonical transform and their applications  

作　　者：DENG Bing TAO Ran 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5期592-603,共12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 Ministerial Foundation of China(Grant No.6140445).

摘　　要：As generalization of the fractional Fourier transform （FRFT）, the linear canonical transform （LCT） has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform （FFT）, which has much lower computational load than the construction method in the linear canonical domain.As generalization of the fractional Fourier transform （FRFT）, the linear canonical transform （LCT） has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform （FFT）, which has much lower computational load than the construction method in the linear canonical domain.

关 键 词：linear canonical transform convolution theorems sampling multiplicative filter. 

分 类 号：TN713[电子电信—电路与系统]