Improving the Performance of Fractional Order Differential Filter by the Fractional Sampling Delay

Abstract

The method of reducing the integral interval by using the fractional order delay filter to improve the performance of fractional differential filter is put forward in this paper. Firstly, in terms of the basic definition of integral the paper generalizes the sampling interval of integral operator from the integral order to fractional order and gets the integral operator whose sampling interval is fractional order. By the Lagrange FIR or IIR fractional delay filter we can transform the fractional order term of the operator obtained above to the integral order term. Then an half sampling delay IIR filter of third order can be chosen as new operator for its better performance. Lastly, the design of fractional order digital filter is implemented by the method of CFE. By the comparative analysis, it is shows that the frequency response of improved fractional order digital differentiator is more close to the ideal fractional order differential filter, which indicates the method put forward in this paper can improve the performance of IIR-type fractional order differential filter obviously.