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Orthogonal Rational Functions and Frequency Analysis
Authors:Haakon Waadeland
Institution:(1) Department of Mathematical Sciences, The Norwegian University of Science and Technology, N-7491 Trondheim, Norway. e-mail
Abstract:One way of finding unknown frequencies in a trigonometric signal is to use Szegodblac theory, where under certain conditions asymptotic behavior of zeros of Szegodblac polynomials lead to the frequencies. Recently this was extended to generalized Szegodblac theory, i.e. where polynomials are replaced by certain rational functions.This note presents a brief overview of some of the Szegodblac 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.
Keywords:orthogonal rational functions  trigonometric signal
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