Insight into Frequency-Domain Extrapolations of Least-Squares-Based Curve Fitting Algorithms

Many efforts have been made in order to identify state-space models of the black-box devices from their terminal admittance/impedance frequency responses. However, the band of the available admittance/impedance frequency responses is some-times relatively narrow, from which some out-of-band critical modes of interest can thus not be intuitively observed. In order to overcome this limitation, the vector fitting (VF) algorithm is used in this paper to identify some out-of-band critical modes of an artificially created rational function. On its basis, the sensitivity index which depicts the effect of the partial fraction term on the in-band fitting error is derived in order to explain the VF’s extrapolation behavior, and its effectiveness is verified on the cases where out-of-band modes of different numbers coexist.