Real orthogonal polynomials in frequency analysis
Abbreviated Journal Title
frequency analysis problem; frequency estimation; orthogonal; polynomials; Szego polynomials; para-orthogonal polynomials; quadrature; SZEGO POLYNOMIALS; UNIT-CIRCLE; CONTINUED FRACTIONS; QUADRATURE; ALGORITHM; ZEROS; Mathematics, Applied
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.
Mathematics of Computation
"Real orthogonal polynomials in frequency analysis" (2004). Faculty Bibliography 2000s. 4224.