On the performance analysis of forward-only and forward-backward matched-filterbank spectral estimators

This paper makes use of a matched-filterbank (MAFI) approach to study the forward-only and forward-backward Capon (termed FCapon and FBCapon, respectively) as well as the forward-only and forward-backward APES (FAPES and FBAPES, respectively) estimators for complex spectral estimation. In particular, we prove that, to within a second-order approximation: (a) FCapon and FBCapon are both biased downward; (b) the bias of FBCapon is half that of FCapon; and (c) FAPES and FBAPES are both unbiased. We also show that computationally the APES estimators are only slightly more involved than the Capon (1969) estimators. A natural and logical conclusion of this paper follows as the preference of APES over the Capon estimators in most applications. Numerical examples are also presented to demonstrate quantitatively the properties of the estimators under study.