IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory

This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional−order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev−Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies.