Science in China Series F: Information Sciences

, Volume 49, Issue 5, pp 592–603

Convolution theorems for the linear canonical transform and their applications


DOI: 10.1007/s11432-006-2016-4

Cite this article as:
Deng, B., Tao, R. & Wang, Y. SCI CHINA SER F (2006) 49: 592. doi:10.1007/s11432-006-2016-4


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.


linear canonical transform convolution theorems sampling multiplicative filter 

Copyright information

© Science in China Press 2006

Authors and Affiliations

  1. 1.Department of Electronic EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Electronic EngineeringNaval Aeronautical Engineering InstituteYantaiChina

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