Variable-order fractional numerical differentiation for noisy signals by wavelet denoising
作者： Yi-Ming Chen , Yan-Qiao Wei , Da-Yan Liu , Driss Boutat , Xiu-Kai Chen
DOI: 10.1016/J.JCP.2016.02.013
关键词:
摘要: In this paper, a numerical method is proposed to estimate the variable-order fractional derivatives of an unknown signal in noisy environment. Firstly, wavelet denoising process adopted reduce noise effect for signal. Secondly, polynomials are constructed fit denoised set overlapped subintervals considered interval. Thirdly, these fitting used as estimations ones, where values obtained near boundaries each subinterval ignored parts. Finally, examples presented demonstrate efficiency and robustness method. An efficient numerically signal.Wavelet signal.Polynomials interval.The based on polynomials.Numerical four cases
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Stphane Mallat, A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way Academic Press. ,(2008)
Wilfrid Perruquetti, Da-Yan Liu, Olivier Gibaru, Taous-Meriem Laleg-Kirati, Fractional Order Numerical Differentiation with B-Spline Functions The International Conference on Fractional Signals and Systems 2013. ,(2013)
Gabriel Peyré, S. G. Mallat, A Wavelet Tour of Signal Processing : The Sparse Way Elsevier/Academic Press. ,(2008)
Francesco Mainardi, Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics arXiv: Statistical Mechanics. ,(2001)
Ronald L. Bagley, Peter J. Torvik, Fractional calculus in the transient analysis of viscoelastically damped structures AIAA Journal. ,vol. 23, pp. 918- 925 ,(1985) , 10.2514/3.9007
Yuriy A. Rossikhin, Marina V. Shitikova, Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids Applied Mechanics Reviews. ,vol. 50, pp. 15- 67 ,(1997) , 10.1115/1.3101682
Mohsen Zayernouri, George Em Karniadakis, Fractional spectral collocation methods for linear and nonlinear variable order FPDEs Journal of Computational Physics. ,vol. 293, pp. 312- 338 ,(2015) , 10.1016/J.JCP.2014.12.001
S. Shen, F. Liu, J. Chen, I. Turner, V. Anh, Numerical techniques for the variable order time fractional diffusion equation Applied Mathematics and Computation. ,vol. 218, pp. 10861- 10870 ,(2012) , 10.1016/J.AMC.2012.04.047
Aytac Arikoglu, Ibrahim Ozkol, Solution of fractional integro-differential equations by using fractional differential transform method Chaos, Solitons & Fractals. ,vol. 40, pp. 521- 529 ,(2009) , 10.1016/J.CHAOS.2007.08.001
Abbas Saadatmandi, Bernstein operational matrix of fractional derivatives and its applications Applied Mathematical Modelling. ,vol. 38, pp. 1365- 1372 ,(2014) , 10.1016/J.APM.2013.08.007