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

• AcceptedAug 30, 2018
• PublishedFeb 20, 2019
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### 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).

Appendixes A–D.

### References

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• 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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