Rational modeling by pencil-of-functions method

Pole-zero modeling of low-pass signals, such as an electromagnetic-scatterer response, is considered in this paper. 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 response 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 ofa scatterer. The paper also includes very recent and tantalizing 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 sample variance for the particular data frame, and then performs the subtraction from the Gram matrix.