Design of variable fractional order differentiator using expansion of hyperbolic function

In this paper, the design of variable fractional order differentiator (VFOD) using expansion of hyperbolic function is presented. First, the ideal frequency response is decomposed into the sum of hyperbolic cosine and sine functions. Then, the power series expansions of hyperbolic functions are used to implement VFOD. The proposed VFOD requires less storage requirement of filter coefficients and implementation complexity than the conventional Farrow structure at cost of longer filter delay. Finally, the numerical examples are demonstrated to show the effectiveness of the proposed design approaches.