A theoretical framework for a class of frequency estimation algorithms

Abstract

This paper discusses a general class of algorithms for estimating the frequencies of a set of complex exponentials, and presents a corrected proof of the validity of the algorithms when applied to either real or complex data. The linear-prediction least-squares algorithms, involve the formulation of the estimation problem in terms of finding the roots of a polynomial in C(x) (the vector space of polynomials over the complex numbers C) that has minimum norm with respect to some inner product defined over C(x).<>