Title

Real Orthogonal Polynomials In Frequency Analysis

Keywords

Frequency analysis problem; Frequency estimation; Orthogonal polynomials; Para-orthogonal polynomials; Quadrature; Szego″ polynomials

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.

Publication Date

1-1-2005

Publication Title

Mathematics of Computation

Volume

74

Issue

249

Number of Pages

341-362

Document Type

Article

Personal Identifier

scopus

DOI Link

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

Socpus ID

11244336954 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/11244336954

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