Time-fractional diffusion equation for signal smoothing

Yuanlu Li, Fawang Liu, Ian W. Turner and Tao Li

Applied Mathematics and Computation, 2018, vol. 326, issue C, 108-116

Abstract: The time-fractional diffusion equation is used for signal smoothing. Compared to the classical diffusion equation, the time-fractional diffusion equation has another adjustable time-fractional derivative order to control the diffusion process. Therefore, some simulated signals are used to compare the smoothing performance between the time-fractional diffusion equation and the classical diffusion equation as well as between classical smoothing methods (regularization method, Savitzky–Golay method and wavelet method). In the end, the time-fractional diffusion filtering is applied in an NMR spectrum smoothing. Results indicate that the time-fractional diffusion filtering is advantage over the classical diffusion filtering and their smoothing performance is better than that of classical smoothing methods.

Keywords: Fractional calculus; Fractional diffusion equation; Difference method; Smoothing (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:326:y:2018:i:c:p:108-116

DOI: 10.1016/j.amc.2018.01.007

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