Orthogonal Rational Functions and Frequency Analysis

One way of finding unknown frequencies in a trigonometric signal is to use Szeg theory, where under certain conditions asymptotic behavior of zeros of Szeg polynomials lead to the frequencies. Recently this was extended to generalized Szeg theory, i.e. where polynomials are replaced by certain rational functions.This note presents a brief overview of some of the Szeg theory, including also a general formula for the monic orthogonal rational functions. Moreover, for a certain measure, constructed from the observations of the signal, the moments are explicitely determined.Finally a simple example is included, indicating the connection between location of an interpolation point and the way zeros approach frequency points.