Generalized Pencil-of-Function Method for Extracting Poles of an EM System from Its Transient Response

A generalized pencil-of-function (GPOF) method for extracting the poles of an EM system from its transient response is developed. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. This is in contrast to the conventional Prony and pencil-of-function methods which yield the solution in two steps, namely, the solution of an ill-conditioned matrix equation and finding the roots of a polynomial. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is also presented.