Design of adjustable fractional order differentiator using expansion of ideal frequency response

In this paper, the design and implementation structures of adjustable fractional order differentiator (AFOD) are presented. First, the series expansion of ideal frequency response is used to transform the design of AFOD into the designs of log differentiators with various orders. Then, conventional FIR filter design method is applied to design log differentiators. The proposed method is flexible because the AFOD can be designed by considering the trade-off among the storage requirement of filter coefficients, implementation complexity and delay of filter. Finally, several numerical examples are shown to illustrate the effectiveness of the proposed design approach.

► This research is a branch of fractional calculus. ► Adjustable fractional order differentiator is designed. ► Four efficient implementation structures are proposed. ► The parameters of 1/f noise can be easily estimated.