Improved design of IIR-type digital fractional-order differentiators using continuous fraction expansion

In this paper, a digital fractional-order differentiator is designed by using continuous fraction expansion method. In that, transfer function is realized for IIR-type fractional order differentiator (FOD) of three kinds (based on Euler, Tustin and Al-Alaoui operators respectively). Further, time domain analysis of these FODs has been performed and then compared with each other. In our analysis, we found that IIR-type digital FOD based on Al-Alaoui operator provide faster convergence among others. The FOD system based on Al-Alaoui operator exhibit 70.67% and 23.52% lesser convergence time as compared to system based on Tustin and Euler operator respectively.