Design of digital Feller fractional order integrator

In this paper, the design problems of the digital Feller fractional order integrator (FOI) are presented. First, the continuous-time fractional order integrals are reviewed briefly. Then, the fact that the frequency response of Feller FOI is linear combination of frequency responses of the conventional FOI is shown. Based on this fact, the conventional FOI is applied to design fixed Feller FOI including trapezoidal integration rule and Simpson integration rule methods. Next, the fractional sample delay is used to improve the designed Feller FOI and the discussion on the variable Feller FOI design is made. Finally, the relation between Feller FOI and fractional Hilbert transformer is studied and the application examples are demonstrated to show the effectiveness of the proposed digital Feller fractional order integrators.