Asymptotics for zeros of Szeg polynomials associated with trigonometric polynomial signals

The study of Wiener-Levinson digital filters leads to certain classes of polynomials orthogonal on the unit circle (Szeg polynomials). Here we present theorems that show that the unknown frequencies in a periodic discrete time signal can be determined from the limiting behavior (as N → ∞) of the zeros of fixed degree Szeg polynomials that are orthogonal with respect to a distribution defined from N successive samples of the signal. This proves an essential part of a conjecture due to Jones, Njåstad, and Saff concerning the frequency analysis problem.