Abstract
This paper contributes a relatively broader realm of new improved rational approximations based on Halley’s iterative method incorporating different orders of one-half, one-third and one-fourth fractional order integrators (FOIs) and fractional order differentiators (FODs) when conceived by existing first and higher order s-to-z transformations for indirect discretisation. The proposed approach has been observed to gear up towards more efficient discretised models when compared with those of existing well established approximation techniques namely continued fraction expansion (CFE) and power series expansion (PSE). Responses of proposed models of FOIs/differentiators based on Al-Alaoui operator and new optimised four segment operator have been reported to have relative magnitude error (dB) as low as –40 dB and linear phase curves in almost full band of normalised frequency. FOIs and FODs based on Tustin operator have presented constant phase response in full range resulting in tremendous improvement over phase responses of its respective existing models.
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