Fractional Calculus in Non-stationary Signal Analysis

Non-stationary signals analysis is an important issue in many fields. However, traditional integer order calculus cannot effectively handle non-stationary signals. This article focused on the application of fractional calculus in non-stationary signal analysis, and proposed a method for processing non-stationary signals based on fractional derivative and fractional integral. The numerical calculation method was taken as the main research means. The difference between fractional calculus and traditional integer calculus as analyzed. The simulation results showed that fractional wavelet transform (FWT) was used to process non-stationary drawings, and the mean square error value was much smaller than the mean square error of traditional Hilbert-Huang transform (HHT). Compared with FWT, HHT had more than 36% of the mean square error of the signal in the process of processing non-stationary signals, and the maximum signal-to-noise ratio of the peak was less than 5% of that of FWT. Therefore, FWT can better depict the complexity and diversity of the long memory signal. In addition, fractional calculus can better reflect the non-linear characteristics of the signal, and provide a more comprehensive signal analysis and modeling method.