Signal, Image and Video Processing

, Volume 8, Issue 1, pp 143–148 | Cite as

Sampling expansion in function spaces associated with the linear canonical transform

  • Xiaoping LiuEmail author
  • Jun Shi
  • Xuejun Sha
  • Naitong Zhang
Original Paper


In this paper, we investigate sampling expansion for the linear canonical transform (LCT) in function spaces. First, some properties of the function spaces related to the LCT are obtained. Then, a sampling theorem for the LCT in function spaces with a single-frame generator is derived by using the Zak Transform and its generalization to the LCT domain. Some examples are also presented.


Linear canonical transform Riesz bases Frames Function spaces Sampling theorem 



This work was supported in part by the National Basic Research Program of China (Grant No. 2013CB329003) and the National Natural Science Foundation of China (Grant No. 61171110).


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Xiaoping Liu
    • 1
    Email author
  • Jun Shi
    • 1
  • Xuejun Sha
    • 1
  • Naitong Zhang
    • 1
    • 2
  1. 1.Communication Research CenterHarbin Institute of TechnologyHarbinChina
  2. 2.Shenzhen Graduate SchoolHarbin Institute of TechnologyShenzhenChina

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