Applications of Szegö polynomials to digital signal processing

DOI10.1216/rmjm/1181073015zbMath0729.94002OpenAlexW2015097129MaRDI QIDQ807588

Olav Njåstad, William B. Jones

Publication date: 1991

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181073015

zbMATH Keywords

Szegö polynomialsfilterdigital signal processingmoment theorytwo-point Padé approximantsfrequency analysis problem

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Padé approximation (41A21) Application of orthogonal and other special functions (94A11) Trigonometric moment problems in one variable harmonic analysis (42A70)

Related Items (19)

Survey article: continued fractions associated with Wiener-Levinson filters, frequency analysis, moment theory and polynomials orthogonal on the unit circle ⋮ Generalized Szegö theory in frequency analysis ⋮ Szegö polynomials associated with Wiener-Levinson filters ⋮ 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 ⋮ Parameter estimation and signal reconstruction ⋮ Asymptotic properties of zeros of orthogonal rational functions ⋮ Asymptotics for zeros of Szegő polynomials associated with trigonometric polynomial signals ⋮ Asymptotics for Szegö polynomial zeros ⋮ PC-fractions and Szegö polynomials associated with starlike univalent functions ⋮ Signal recovery by discrete approximation and a Prony-like method ⋮ Asymptotics for Orthogonal Rational Functions ⋮ Szegő polynomials applied to frequency analysis ⋮ Product rules on the unit circle with uniformly distributed nodes. Error bounds for analytic functions ⋮ Distribution of roots of random real generalized polynomials ⋮ Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle

Cites Work

• A constructive proof of convergence of the even approximants of positive PC-fractions
• The Schur algorithm and its applications
• Continued fractions associated with trigonometric and other strong moment problems
• Asymptotically fast solution of Toeplitz and related systems of linear equations
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• Superfast Solution of Real Positive Definite Toeplitz Systems
• The Numerical Stability of the Levinson-Durbin Algorithm for Toeplitz Systems of Equations
• Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences
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