Abstract
This work introduces a new realization method of fractional-order integrators (FOI) and differentiators (FOD) of complex orders. The corresponding Laplace variables of the form S±α±jβ; 0 < α, β ≤ 1, are approximated and realized via minimum-phase rational transfer functions within a frequency band. The realization is adaptive since it depends on the frequency band of operation. Proper selection of the complex order and its sign play an important role in widening up and improving the phase diagram of the approximation at high frequency. Thus, making them ideal candidates to improve the leading phase of the FOI/FOD at high frequency. The main points of this work are verified via numerical simulations.
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