Szegő polynomials applied to frequency analysis

DOI10.1016/0377-0427(93)90297-OzbMath0784.65105MaRDI QIDQ1802169

William B. Jones, Haakon Waadeland, Olav Njåstad, W. J. Thron

Publication date: 11 August 1993

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergencePadé approximantsSzegö polynomialsfrequency analysisLevinson's algorithmdiscrete signalsWiener- Levinson methodWiener-Levinson filters

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Padé approximation (41A21) Numerical methods for trigonometric approximation and interpolation (65T40) Application of orthogonal and other special functions (94A11) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

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Survey article: continued fractions associated with Wiener-Levinson filters, frequency analysis, moment theory and polynomials orthogonal on the unit circle, Sensitivity analysis for Szegő polynomials, A case of Toeplitz determinants and theta functions in frequency analysis, Generalized Szegö theory in frequency analysis, Real orthogonal polynomials in frequency analysis, Orthogonal matrix polynomials and applications, On the method of finding frequencies with large amplitudes, Orthogonal Laurent polynomials on the unit circle, extended CMV ordering and 2D Toda type integrable hierarchies, Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems, Convergence of PPC-continued fraction approximants in frequency analysis, Para-orthogonal polynomials in frequency analysis, Modifications of the moments in frequency analysis, Univalent functions and frequency analysis, Parameter estimation and signal reconstruction, Weak convergence and boundedness properties of measures in frequency analysis, Asymptotic properties of zeros of orthogonal rational functions, Asymptotics for zeros of Szegő polynomials associated with trigonometric polynomial signals, Asymptotics for Szegö polynomial zeros, Signal recovery by discrete approximation and a Prony-like method, Modification of a method using Szegő polynomials in frequency analysis: The \(V\)-process, Zeros of Sobolev orthogonal polynomials on the unit circle, Asymptotic behavior of Szegö polynomials, OPUC, CMV matrices and perturbations of measures supported on the unit circle, Continuation methods for the computation of zeros of Szegő polynomials, On measures in frequency analysis, Multiple zeros in frequency analysis: The \(T(r)\)-process, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle

Cites Work

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• A constructive proof of convergence of the even approximants of positive PC-fractions
• Applications of Szegö polynomials to digital signal processing
• Continued fractions associated with trigonometric and other strong moment problems
• Asymptotics for zeros of Szegő polynomials associated with trigonometric polynomial signals
• Szegö polynomials associated with Wiener-Levinson filters
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• Linear Prediction of Speech
• Anharmonic Frequency Analysis