Continued Fractions and Szegö Polynomials in Frequency Analysis and Related Topics
作者： William B. Jones , Vigdis Petersen
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摘要: This paper is an expository survey of recent research on the application Szego polynomials and PPC-continuedfractions to frequency analysis problem described as follows: We want determine unknown frequencies ω1, ω2, ..., ω I from a sample N observed values x (m), m = 0, 1, N− arising continuous waveform that superposition finite number sinusoidal waves with ω1,ω2, . The method based property certain zerosof (and poles PPC-fraction approximants) converge (as → ∞) points ei j , ±1, ± 2, I. remaining zeros are bounded away unit circle |z|=1, asN ∞. Levinson algorithm used construct PPC-fractions (m). A discussion given connections between topics: Caratheodory functions,the trigonometric moment problem, PPC-fractions. also describe applications Doppler radar, medicine, speech processing, therapy, meteorology ocean tides.
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