The relationship between maximum entropy and maximum likelihood spectra

Abstract

Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If [Formula: see text], j = 0, 1,… M − 1 and M successive maximum entropy spectral density estimates at frequency f, then the M‐length maximum likelihood spectral density estimate [Formula: see text] is given by [Formula: see text]. (1) The maximum entropy estimates are made via Burg's well‐known formula,[Formula: see text], (2) where [Formula: see text], k = 0, 1,…,N are the coefficients of the N‐length prediction‐error filter, [Formula: see text] is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).