On spectral and root forms of sinusoidal frequency estimators

Two forms for retrieving sinusoidal frequencies from an estimated characteristic polynomial, the root form and the spectral form, are examined. It is proved that both forms give frequency estimates with the same asymptotic covariance matrix, regardless of the (consistent) method used to estimate the characteristic polynomial. The finite sample case is examined by means of Monte Carlo simulations for a specific method used to estimate the characteristic polynomial. It is shown that the root form has a distinctly smaller failure rate than the spectral form. However, it is shown that in the successful realizations the forms have nearly identical mean square errors