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Application of the Local Fractional Fourier Series to Fractal Signals

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Discontinuity and Complexity in Nonlinear Physical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 6))

Abstract

Local fractional Fourier series is a generalized Fourier series in fractal space. The local fractional calculus is one of useful tools to process the local fractional continuously non-differentiable functions (fractal functions). Based on the local fractional derivative and integration, the present chapter is devoted to the theory and applications of local fractional Fourier analysis in generalized Hilbert space. We recall the local fractional Fourier series, the Fourier transform, the generalized Fourier transform, the discrete Fourier transform and fast Fourier transform in fractal space.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu, 221008, China

    Xiao-Jun Yang

  2. Institute of Software Science, Zhengzhou Normal University, Zhengzhou, 450044, China

    Xiao-Jun Yang

  3. Institute of Applied mathematics, Qujing Normal University, Qujing, 655011, China

    Xiao-Jun Yang

  4. Faculty of Engineering, Department of Chemical and Materials Engineering, King Abdulaziz University, 80204, Jeddah, 21589, Saudi Arabia

    Dumitru Baleanu

  5. Faculty of Arts and Sciences, Department of Mathematics and Computer Sciences, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  6. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

  7. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

Authors
  1. Xiao-Jun Yang
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  2. Dumitru Baleanu
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  3. J. A. Tenreiro Machado
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Corresponding author

Correspondence to Xiao-Jun Yang .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Polytechnic Institute of Porto Institute of Engineering, Porto, Portugal

    J. A. Tenreiro Machado

  2. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

    Albert C J Luo

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© 2014 Springer International Publishing Switzerland

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Yang, XJ., Baleanu, D., Machado, J.A.T. (2014). Application of the Local Fractional Fourier Series to Fractal Signals. In: Machado, J., Baleanu, D., Luo, A. (eds) Discontinuity and Complexity in Nonlinear Physical Systems. Nonlinear Systems and Complexity, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-01411-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-01411-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01410-4

  • Online ISBN: 978-3-319-01411-1

  • eBook Packages: EngineeringEngineering (R0)

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