Application of the local fractional Fourier series to fractal signals. (English) Zbl 1319.42005
Machado, José A. Tenreiro (ed.) et al., Discontinuity and complexity in nonlinear physical systems. Selected papers based on the presentations at the 4th international conference on nonlinear science and complexity, NSC, Budapest, Hungary, August 6–11, 2012. Cham: Springer (ISBN 978-3-319-01410-4/hbk; 978-3-319-01411-1/ebook). Nonlinear Systems and Complexity 6, 63-89 (2014).
Summary: A local fractional Fourier series is a generalized Fourier series in fractal spaces. The local fractional calculus is one of the 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 spaces. We recall the local fractional Fourier series, the Fourier transform, the generalized Fourier transform, the discrete Fourier transform and fast Fourier transform in fractal spaces.
For the entire collection see [Zbl 1280.37003].
For the entire collection see [Zbl 1280.37003].
MSC:
| 42A99 | Harmonic analysis in one variable |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 26A33 | Fractional derivatives and integrals |
| 26A36 | Antidifferentiation |
| 28A80 | Fractals |
Keywords:
local fractional Fourier series; local fractional calculus; local fractional Fourier transform; fractal spaceReferences:
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