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SCIENCE CHINA Information Sciences, Volume 62, Issue 4: 049301(2019) https://doi.org/10.1007/s11432-018-9585-1

Digital computation of linear canonical transform for local spectra with flexible resolution ability

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  • ReceivedMar 22, 2018
  • AcceptedAug 30, 2018
  • PublishedFeb 20, 2019

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61671063) and Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 61421001).


Supplement

Appendixes A–D.


References

[1] Collins S A. Lens-System Diffraction Integral Written in Terms of Matrix Optics. J Opt Soc Am, 1970, 60: 1168-1177 CrossRef Google Scholar

[2] Xu T Z, Li B Z. Linear Canonical Transform and its Application. Beijing: Science Press, 2013. 291--324. Google Scholar

[3] Healy J J, Kutay M A, Ozaktas H M, et al. Linear Canonical Transform: Theory and Applications. New York: Springer, 2016. 197--240. Google Scholar

[4] Hennelly B M, Sheridan J T. Fast numerical algorithm for the linear canonical transform. J Opt Soc Am A, 2005, 22: 928-937 CrossRef ADS Google Scholar

[5] Koc A, Ozaktas H M, Candan C. Digital Computation of Linear Canonical Transforms. IEEE Trans Signal Process, 2008, 56: 2383-2394 CrossRef ADS Google Scholar

[6] Pei S C, Huang S G. Fast Discrete Linear Canonical Transform Based on CM-CC-CM Decomposition and FFT. IEEE Trans Signal Process, 2016, 64: 855-866 CrossRef ADS arXiv Google Scholar

[7] Goertzel G. An Algorithm for the Evaluation of Finite Trigonometric Series. Am Math Mon, 1958, 65: 34-35 CrossRef Google Scholar

  • Table 1   The properties of ZDLCT
    Linear property$L_{A}[(ax_{1}(n)+bx_{2}(n))](T_{u}^{\lambda,P}) =aL_{A}[x_{1}(n)](T_{u}^{\lambda,P})+bL_{A}[x_2(n)](T_{u}^{\lambda,P})$
    Reverse property$L_{A}[x(-n)](T_{u}^{\lambda,P})=L_{A}[x(n)][-(T_{u}^{\lambda,P})]$
    Odd-even property$~L_{A}\left[x(n)\right](T_{u}^{\lambda,P})=L_{A}[x(n)][-(T_{u}^{\lambda,P})]$ ,
    or $L_{A}\left[x(n)\right](T_{u}^{\lambda,P})=-L_{A}\left[x(n)\right][-(T_{u}^{\lambda,P})~]$
    Modulation property$L_{A}\left[x(n){\rm~e}^{{\rm~j}2\pi\mu~nT}\right](T_{u}^{\lambda,P}) ={\rm~e}^{-{\rm~j}\pi\alpha\frac{\mu^2}{\beta^2}}{\rm~e}^{{\rm~j}2\pi\alpha~T_{u}^{\lambda,P}\frac{\mu}{\beta}}\times~L_{A}[x(n)](T_{u}^{\lambda,P}-\frac{\mu}{\beta})$

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