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Convolution, correlation, and sampling theorems for the offset linear canonical transform

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Abstract

The offset linear canonical transform (OLCT), which is a time-shifted and frequency-modulated version of the linear canonical transform, has been shown to be a powerful tool for signal processing and optics. However, some basic results for this transform, such as convolution and correlation theorems, remain unknown. In this paper, based on a new convolution operation, we formulate convolution and correlation theorems for the OLCT. Moreover, we use the convolution theorem to investigate the sampling theorem for the band-limited signal in the OLCT domain. The formulas of uniform sampling and low-pass reconstruction related to the OLCT are obtained. We also discuss the design method of the multiplicative filter in the OLCT domain. Based on the model of the multiplicative filter in the OLCT domain, a practical method to achieve multiplicative filtering through convolution in the time domain is proposed.

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Authors and Affiliations

  1. College of Automation, University of Electronic Science and Technology of China, Chengdu, 610054, People’s Republic of China

    Qiang Xiang

  2. College of Electrical and Information, Southwest University for Nationalities, Chengdu, 610041, People’s Republic of China

    Qiang Xiang

  3. Institute of Astronautics and Aeronautics, University of Electronic Science and Technology of China, Chengdu, 610054, People’s Republic of China

    KaiYu Qin

Authors
  1. Qiang Xiang
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  2. KaiYu Qin
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Correspondence to Qiang Xiang.

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Xiang, Q., Qin, K. Convolution, correlation, and sampling theorems for the offset linear canonical transform. SIViP 8, 433–442 (2014). https://doi.org/10.1007/s11760-012-0342-0

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  • DOI: https://doi.org/10.1007/s11760-012-0342-0

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