Real orthogonal polynomials in frequency analysis - Bracciali, Cleonice Fátima [UNESP]; Li, X; Ranga, A. S. (Amer Mathematical Soc, 2004)
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; Szego polynomials; para-orthogonal polynomials; quadrature