Survey Article: Continued fractions associated with Wiener-Levinson filters, frequency analysis, moment theory and polynomials orthogonal on the unit circle

Abstract

This paper surveys the close relationships among the topics included in the title. Emphasis is given to the family of positive Perron-Caratheodory continued fractions (PPC-fractions) which play a central role in the theory of trigonometric moment problems and Szego polynomials orthogonal on the unit circle. An important application of PPC-fractions is frequency analysis of discrete time signals using Wiener-Levinson digital filters with illustrations given from computational experiments.