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Real orthogonal polynomials in frequency analysis |
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| Authors: | C. F. Bracciali Xin Li 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 Xin Li ; Department of Mathematics, University of Central Florida, Orlando, Florida 32816 A. Sri Ranga ; Departamento de Ciências de Computação e Estatística, IBILCE, UNESP- Universidade Estadual Paulista, 15054-000 São José do Rio Preto, São Paulo, Brazil |
| 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. |
| Keywords: | Frequency analysis problem frequency estimation orthogonal polynomials SzegH{o} polynomials para-orthogonal polynomials quadrature |
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