Employing symmetry constraints for improved frequency estimation by eigenanalysis methods

Abstract

The problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered. Eigenanalysis methods, such as Pisarenko’s method and the extended Prony method, find the eigenvector with minimum eigenvalue of a suitably chosen matrix and then obtain the complex sinusoids as the roots of the polynomial that has the components of the eigenvector as coefficients. For the sinusoids to be undamped, it is necessary that the roots lie on the unit circle and hence that the eigenvector be conjugate symmetric. It is shown how this symmetry constraint can be incorporated into eigenanalysis estimation methods in a routine way. The practical importance of the constraint is ..