Rational Modeling by Pencil-of-Functions Method

Pole-zero modeling of signals, such as an electromagnetic-scatterer response, is considered in this paper. It is shown by use of the pencil-of-functions theorem that a) the true parameters can be recovered in the ideal case [where the signal is the impulse reponse of a rational function H(z)], and b) the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error. Although the computations are more involved than in all-pole modeling, they are considerably less than those required in iterative schemes of pole-zero modeling. The advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer. The paper also includes very recent and promising results on a new approach to noise correction. In contradistinction with spectral subtraction techniques, where only amplitude information is emphasized (and phase is ignored), we propose a method that a) estimates the noise spectral density for the data frame, and then b) performs the subtraction of the noise correlation matrix from the Gram matrix of the signal.