TRANSMISSION-LINE MODELS FOR THE MODIFIED SCHUR-ALGORITHM

We present 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. 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. We show that these three problems can be solved using the transmission-line models and their physical properties such as causality and energy conservation.