Numerical extraction of Cole-Cole impedance parameters from step response

In this paper we propose a numerical method to extract the four parameters (R-0, R-infinity, C, and alpha) that characterize a single-dispersion Cole-Cole impedance model from its step response, based on modelling the step response using fractional calculus, without requiring direct measurement of the real and imaginary impedance parts. MATLAB simulations using Cole-Cole impedances of fruit tissues with alpha < 1, PSPICE simulations and experimental results using a Cole-Cole model with alpha = 1 are given to verify the method. Extracted impedance parameters show less than 0.1% relative error in simulation and less than 10% error in experimental results for the extracted impedance parameters.