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Real orthogonal polynomials in frequency analysis

Authors: C. F. Bracciali, Xin Li and A. Sri Ranga
Journal: Math. Comp. 74 (2005), 341-362
MSC (2000): Primary 42C05, 94A11, 94A12
Published electronically: May 25, 2004
MathSciNet review: 2085896
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.

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Additional Information

C. F. Bracciali
Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, UNESP- Universidade Estadual Paulista, 15054-000 São José do Rio Preto, São Paulo, Brazil

Xin Li
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816

A. Sri Ranga
Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, UNESP- Universidade Estadual Paulista, 15054-000 São José do Rio Preto, São Paulo, Brazil

Keywords: Frequency analysis problem, frequency estimation, orthogonal polynomials, Szeg\H{o} polynomials, para-orthogonal polynomials, quadrature
Received by editor(s): March 8, 2003
Received by editor(s) in revised form: August 14, 2003
Published electronically: May 25, 2004
Additional Notes: This research was started while the second author was visiting the campus of UNESP at São José do Rio Preto, during September/October 2002, with a Fellowship from FAPESP. The first and the third authors’ research is supported by grants from CNPq and FAPESP
Article copyright: © Copyright 2004 American Mathematical Society