A Fractional-Order Digital Filter Implementation Method

Fractional-order digital filters have broad application prospects in the data processing of nonlinear systems. This paper presents a fractional-order digital filter implementation method by the inverse Fourier transform and convolution. The finite sequence of fractional-order low-pass digital filter can be obtained by the inverse Fourier transform of its frequency response function in a finite integration interval and width. The finite sequence of fractional-order high-pass digital filter can be obtained by convolution of the fractional-order low-pass digital filter sequence and the sequence of fractional-order differential operator. The high-pass digital filter of order 1.5 is used as an example to show the related sequence during calculation, and the magnitude response of both the low-pass and high-pass digital filters of order 1.5 is verified through Simulink simulation. Finally, the parameters involved in the method are analyzed for impact on the fractional-order digital filter implementation.