Transmission-line models for the modified Schur algorithm

Transmission-line models for the modified Schur algorithm that handles functions that are bounded on the unit circle and have a finite number of poles inside the unit disc are presented. The first application of these models is the physical interpretation of procedures for root distribution with respect to the unit circle: for every polynomial p(z), the transmission-line model for the all-pass p#(z)/p(z) has a special structure from which the number of stable and unstable zeros can be calculated by inspection. Three other applications are to problems from analytic function theory and linear algebra: the matching of Taylor coefficients; the factorization of certain indefinite Hermitian matrices; and the Schur-Takagi extension problem. It is shown that these three problems can be solved using the transmission-line models and their physical properties such as causality and energy conservation