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This paper surveys the close relationships among the topics included in the title. Emphasis is given to the family of positive Perron-Carathéodory continued fractions (PPC-fractions) which play a central role in the theory of trigonometric moment problems and Szegö 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.

the rocky mountain journal of mathematics/rocky mountain journal of mathematics

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