Poles sequence selection in implementation of fractional-order difference via Takenaka-Malmquist functions

The paper presents a new algorithm for the selection of poles for modeling fractional-order difference based on Takenaka-Malmquist functions. The main advantage of the proposed approach to the selection of poles is better approximation accuracy in the chosen frequency adequacy range as well as in the time domain of finite-length implementation of the Takenaka-Malmquist-base fractional-order difference. The proposed Takenaka-Malmquist-based difference implementation can also be applied to model fractional-order integrators and non-commensurate state-space systems.