Time-fractional diffusion equation for signal smoothing

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.