caa a22 4500 475839102 CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006454131615 doi (NATIONALLICENCE)springer-10.1023/A:1006454131615 Continued Fractions and Szegö Polynomials in Frequency Analysis and Related Topics [Elektronische Daten] [William Jones, Vigdis Petersen] This paper is an expository survey of recent research on the application of Szegö polynomials and PPC-continuedfractions to the frequency analysis problem described as follows: We want to determine the unknown frequencies ω1, ω2, ..., ω I from a sample of N observed values x N (m), m = 0, 1, ..., N− 1, arising from a continuous waveform that is the superposition of a finite number of sinusoidal waves with frequencies ω1,ω2, ..., ω I . The method is based on the property that certain zerosof the Szegö polynomials (and poles of the PPC-fraction approximants) converge (as N → ∞) to the frequency points e i ω j , j = ±1, ± 2, ..., ± I. The remaining zeros are bounded away from the unit circle |z|=1, asN → ∞. The Levinson algorithm is used to construct the Szegö polynomials and PPC-fractions from the values x N (m). A discussion is given on connections between the topics: Carathéodory functions,the trigonometric moment problem, Szegö polynomials and PPC-fractions. We also describe applications to Doppler radar, medicine, speech processing, speech therapy, meteorology and ocean tides. Kluwer Academic Publishers, 2000 frequency analysis nationallicence Szegö polynomials nationallicence continued fractions nationallicence Jones William Department of Mathematics, University of Colorado, 80309-0395, Boulder, CO, U.S.A. aut Petersen Vigdis Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034, Trondheim, Norway. e-mail aut Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 149-174 0167-8019 61:1-3<149 2000 61 10440 https://doi.org/10.1023/A:1006454131615 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006454131615 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jones William Department of Mathematics, University of Colorado, 80309-0395, Boulder, CO, U.S.A aut NATIONALLICENCE 700 1- Petersen Vigdis Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034, Trondheim, Norway. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 149-174 0167-8019 61:1-3<149 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer