| Convolution theorems for the linear canonical transform and their applications |
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| 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.
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| 收稿时间： | 21 March 2005 |
| 修稿时间： | 26 April 2006 |
Convolution theorems for the linear canonical transform and their applications |
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| Authors: | DENG Bing TAO Ran WANG Yue |
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| Affiliation: | 1. Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China;Department of Electronic Engineering, Naval Aeronautical Engineering Institute, Yantai 264001, China
2. Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | 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. |
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| Keywords: | linear canonical transform convolution theorems sampling multiplicative filter |
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