Application of the Local Fractional Fourier Series to Fractal Signals

  • Xiao-Jun YangEmail author
  • Dumitru Baleanu
  • J. A. Tenreiro Machado
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 6)


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.


Local fractional Fourier series Local fractional calculus Local fractional Fourier transform The generalized local fractional Fourier transform Discrete local fractional Fourier transform Fast local fractional Fourier transform Fractal space 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Xiao-Jun Yang
    • 1
    • 2
    • 3
    Email author
  • Dumitru Baleanu
    • 4
    • 5
    • 6
  • J. A. Tenreiro Machado
    • 7
  1. 1.Department of Mathematics and MechanicsChina University of Mining and TechnologyXuzhouChina
  2. 2.Institute of Software ScienceZhengzhou Normal UniversityZhengzhouChina
  3. 3.Institute of Applied mathematicsQujing Normal UniversityQujingChina
  4. 4.Faculty of Engineering, Department of Chemical and Materials EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  5. 5.Faculty of Arts and Sciences, Department of Mathematics and Computer SciencesCankaya UniversityAnkaraTurkey
  6. 6.Institute of Space SciencesMagurele-BucharestRomania
  7. 7.Department of Electrical EngineeringInstitute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 431PortoPortugal

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