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Local Fractional Z‐Transforms with Applications to Signals on Cantor Sets

Author

Listed:
  • Kai Liu
  • Ren-Jie Hu
  • Carlo Cattani
  • Gong-Nan Xie
  • Xiao-Jun Yang
  • Yang Zhao

Abstract

The Z‐transform has played an important role in signal processing. In this paper the Z‐transform has been generalized by the coupling of both the Z‐transform and the local fractional complex calculus. In the literature the local fractional Z‐transform is applied to analyze signals, in the following it will be used to analyze signals on Cantor sets. Some examples are also given to show the efficiency and accuracy for handling the signals on Cantor sets.

Suggested Citation

  • Kai Liu & Ren-Jie Hu & Carlo Cattani & Gong-Nan Xie & Xiao-Jun Yang & Yang Zhao, 2014. "Local Fractional Z‐Transforms with Applications to Signals on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:638648
    DOI: 10.1155/2014/638648
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    References listed on IDEAS

    as
    1. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Yang Zhao & Dumitru Baleanu & Mihaela Cristina Baleanu & De-Fu Cheng & Xiao-Jun Yang, 2013. "Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, October.
    3. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, January.
    4. Yang Zhao & Dumitru Baleanu & Mihaela Cristina Baleanu & De-Fu Cheng & Xiao-Jun Yang, 2013. "Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Sun, HongGuang & Chen, Wen & Li, Changpin & Chen, YangQuan, 2010. "Fractional differential models for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2719-2724.
    6. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-130, November.
    7. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    Cited by:

    1. Yang Li & Long-Fei Wang & Sheng-Da Zeng & Yang Zhao, 2014. "Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).

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