An algorithm for determining global parameters of minimum-phase systems with fractional power spectra

A method to determine the singularities and the corresponding powers of minimum-phase system functions with fractional power spectra from experimental data is presented. The characteristic parameters of the dynamic system are computed from the measured frequency spectrum using the derivative method to obtain an initial estimate of the parameters followed by a least-square optimization technique for fine tuning. Mathematical formulations of the derivative and the optimization steps are discussed, and a comparison between the estimated and theoretical parameters is provided. The simulated and experimental data collected from a polarized metal electrode-electrolyte interface serve to test the performance of the algorithm. Although the algorithm is proposed to extract the global parameters of fractional power spectrum systems, it can also be used to obtain the characteristic parameters of systems with integer power factors