RATIONAL MODELING BY PENCIL-OF-FUNCTIONS METHOD.

Pole-zero modeling of low-pass signals, such as an electromagnetic-scatterer response, is considered. It is shown by use of 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 generalized least-squares 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 simulation example and through application to the electromagnetic response of a scatterer.