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Convolution theorems for the linear canonical transform and their applications

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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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Authors and Affiliations

  1. Department of Electronic Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Deng Bing, Tao Ran & Wang Yue

  2. Department of Electronic Engineering, Naval Aeronautical Engineering Institute, Yantai, 264001, China

    Deng Bing

Authors
  1. Deng Bing
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  2. Tao Ran
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  3. Wang Yue
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Correspondence to Deng Bing.

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Deng, B., Tao, R. & Wang, Y. Convolution theorems for the linear canonical transform and their applications. SCI CHINA SER F 49, 592–603 (2006). https://doi.org/10.1007/s11432-006-2016-4

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  • DOI: https://doi.org/10.1007/s11432-006-2016-4

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