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Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

Author

Listed:
  • Zhi-Yong Chen
  • Carlo Cattani
  • Wei-Ping Zhong

Abstract

From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.

Suggested Citation

  • Zhi-Yong Chen & Carlo Cattani & Wei-Ping Zhong, 2014. "Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:561434
    DOI: 10.1155/2014/561434
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    References listed on IDEAS

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    1. 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.
    2. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Xiao-Jun Yang & Dumitru Baleanu & H. M. Srivastava & J. A. Tenreiro Machado, 2013. "On Local Fractional Continuous Wavelet Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, November.
    4. Xiao-Jun Yang & Dumitru Baleanu & H. M. Srivastava & J. A. Tenreiro Machado, 2013. "On Local Fractional Continuous Wavelet Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
    6. 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).
    7. Nigmatullin, R.R. & Osokin, S.I. & Toboev, V.A., 2011. "NAFASS: Discrete spectroscopy of random signals," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 226-240.
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