caa a22 4500 475838912 CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006417408359 doi (NATIONALLICENCE)springer-10.1023/A:1006417408359 Waadeland Haakon Department of Mathematical Sciences, The Norwegian University of Science and Technology, N-7491, Trondheim, Norway. e-mail aut Orthogonal Rational Functions and Frequency Analysis [Elektronische Daten] [Haakon Waadeland] One way of finding unknown frequencies in a trigonometric signal is to use Szegő theory, where under certain conditions asymptotic behavior of zeros of Szegő polynomials lead to the frequencies. Recently this was extended to generalized Szegő theory, i.e. where polynomials are replaced by certain rational functions. This note presents a brief overview of some of the Szegő 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. Kluwer Academic Publishers, 2000 orthogonal rational functions nationallicence trigonometric signal nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 367-377 0167-8019 61:1-3<367 2000 61 10440 https://doi.org/10.1023/A:1006417408359 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006417408359 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Waadeland Haakon Department of Mathematical Sciences, The Norwegian University of Science and Technology, N-7491, Trondheim, Norway. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 367-377 0167-8019 61:1-3<367 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer