Thiele’s continued fractions in digital implementation of noninteger differintegrators

A rational approximation is the preliminary step of all the indirect methods for implementing digital fractional differintegrators s^nu, with nu in R, 0 < |nu| < 1, and where s in C. This paper employs the convergents of two Thiele’s continued fractions as rational approximations of s^nu. In a second step, it uses known s-to-z transformation rules to obtain a rational, stable, and minimum-phase z-transfer function,with zeros interlacing poles. The paper concludes with a comparative analysis of the quality of the proposed approximations in dependence of the used s-to-z transformations and of the sampling period.