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Variable-order fractional numerical differentiation for noisy signals by wavelet denoising

Abstract : In this paper, an efficient method is proposed to numerically estimate the variable-order fractional derivatives of a noisy signal. Firstly, the process of wavelet denoising is adopted to reduce the noise effect in the signal. Secondly, polynomials are constructed to fit the denoised signal in a set of overlapped subintervals of the considered interval. Thirdly, the variable-order fractional derivatives of these fitting polynomials are considered as the estimations of the original signal, where the values obtained near the boundaries of each subinterval are ignored in the overlapped parts. Finally, numerical examples are presented to demonstrate the efficiency and robustness of the proposed method.
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https://hal.archives-ouvertes.fr/hal-02884938
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Submitted on : Tuesday, June 30, 2020 - 11:39:19 AM
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Yi-Ming Chen, Yan-Qiao Wei, Da-Yan Liu, Driss Boutat, Xiu-Kai Chen. Variable-order fractional numerical differentiation for noisy signals by wavelet denoising. Journal of Computational Physics, Elsevier, 2016, 311, pp.338-347. ⟨10.1016/j.jcp.2016.02.013⟩. ⟨hal-02884938⟩

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