Design of variable fractional order differentiator using infinite product expansion

In this paper, the design of variable fractional order differentiator (VFOD) using the infinite product expansion is presented. First, the infinite products of hyperbolic cosine and sine functions are applied to transform the VFOD design into the designs of first and second order digital log differentiators. Then, the FIR log differentiators designed by least-squares method are used to implement the proposed VFOD efficiently. The main advantage of the proposed VFOD is that it needs less storage requirement of filter coefficients than the traditional power series expansion design approach. Finally, several numerical examples are demonstrated to show the effectiveness of the proposed design method.