Design of digital Riesz fractional order differentiator

In this paper, the design problems of the digital Riesz fractional order differentiator (FOD) are presented. First, the continuous-time Riesz fractional order derivative is reviewed briefly. Then, the fact that the frequency response of Riesz FOD is only the scaling even part of frequency response of the conventional FOD is shown. Based on this fact, the conventional FOD are applied to design fixed Riesz FOD including fractional differencing method, Tustin׳s method and discrete cosine transform method. Next, the fractional sample delay is used to improve the designed Riesz FOD. And, the discussion on the variable Riesz FOD design and implementation issues are made. Finally, numerical and application examples are demonstrated to show the effectiveness of the proposed digital Riesz fractional order differentiators.