New interpretations for the MLM and DASE spectral estimators

This paper provides new interpretations for two modern spectral estimators, the Data Adaptive Spectral Estimator (DASE) of Davis and Regier, and the earlier Maximum Likelihood Method (MLM) of Capon, a special case of DASE. These methods provide estimates for spectral power in some region of frequency space, in terms of an estimate for a correlation matrix. They are conventionally interpreted as window-type spectral estimates, where the window is a function of the estimated correlation matrix. Assuming that the estimated correlation matrix is correct, it is shown that the problem of determining the spectral power is ill-posed. Specifically it is shown that DASE and MLM provide upper bounds on spectral power in some region of frequency space where the spectral density is assumed constant. Furthermore, it is shown that the assumptions and constraints that determine these upper bounds yield trivial lower bounds of zero.