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Summary. Vector Fitting (VF) is an iterative technique to construct rational approximations based on multiple frequency domain samples, introduced by Gustavsen and Semlyen [1,3]. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. Numerical experiments show that VF has favorable convergence properties. However, so far, no theoretical proof for its convergence, or conditions to guarantee convergence, have been published. This paper gives a description of a general iterative Least-Squares framework for rational approximation and shows that VF fits into this framework.

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Vector Fitting is an effective technique for rational approximation of LTI systems. It has been extended to fit the magnitude of the transfer function in absence of phase data. In this paper, magnitude Vector Fitting is modified to work on inequalities which the magnitude of the transfer function has to satisfy, instead of least squares approximation. The new interval version of the magnitude Vector Fitting is proved valuable for multiband filter design and the fitting of noisy magnitude spectra.