The Vector Fitting Algorithm

Summary

This chapter introduces the vector fitting (VF) method for fitting a rational function (model) to a set of frequency‐domain or time‐domain tabulated data. It starts from the linearized rational fitting formulation obtained by weighting, known as Levy's approach. The chapter explains the Sanathanan‐Koerner (SK) iteration, which compensates the undesired weighting within an iterative process. It shows that VF can be interpreted as a pole relocation process, that is, as an iterative refinement of a set of poles that quickly converge to the dominant poles of the system under modeling. Appropriate procedures for order selection, parameter initialization, and stability enforcement and an improvement to the VF convergence properties are discussed. Following the description of classical frequency‐domain vector fitting (FD‐VF), the chapter introduces other formulations of VF, including the time‐domain vector fitting (TD‐VF). Finally, the chapter talks about the z‐domain vector fitting (ZD‐VF), orthonormal vector fitting (OVF) and some special variants.