Properties of the maximum likelihood and pisarenko spectral estimates

The performance of the maximum likelihood spectral estimate is compared vis-à-vis the classical Bartlett spectrum. Asymptotic behavior and special cases such as single tone harmonic analysis are considered. Also, the Pisarenko method of harmonic retrieval is analyzed for the case of a single tone imbedded in noise. The statistical properties of the eigenvector corresponding to the minimum eigenvalue as well as that of the estimated frequency value are derived. The dependence of the reliability of the estimate upon the data size and the tone frequency location is illustrated.