The Generalized Pencil-Of-Function (GPOF) Method for Extracting Poles from Transient Responses

Abstract

The generalized penci1-of-function (GPOF) method for extracting the poles of EM (electromagnetic) systems from their transient responses is presented. The GPOF method solves a generalized eigenvalue problem to find the poles. This is in contrast to the conventional Prony and Penci1-of- Function (POF) methods which yield the solution in two steps, namely, the solution of an ill-conditioned matrix equation and finding the roots of a polynomial. To optimize the performance of the GPOF method, the subspace decomposition approach is used. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and it approaches the Cramer-Rao bound when SNR is above threshold. To further lower the threshold of the GPOF method, a circular weighting matrix is proposed. An application of the GPOF method to a thin-wire target is also presented.