Design of digital fractional order differentiator using discrete sine transform

In this paper, the designs of digital fractional order differentiator (DFOD) using discrete sine transforms (DST) are presented. First, the definition of fractional differentiation is reviewed briefly. Then, the DST-based interpolation method is applied to compute the fractional differentiation of a given digital signal. Next, the transfer functions of DFOD are obtained from the DST computational results by using index mapping method. Finally, some numerical and application examples are demonstrated to show the effectiveness of the proposed DST-based design method.