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

DOI:
https://doi.org/10.1090/S0025-5718-04-01672-2

Published electronically:
May 25, 2004

MathSciNet review:
2085896

Full-text PDF Free Access

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

DOI:
https://doi.org/10.1090/S0025-5718-04-01672-2

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