The relationship between maximum entropy and maximum likelihood spectra

Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If S_E(f,j), 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 S_L(f,M) is given by The maximum entropy estimates are made via Burg's well-known formula, where γ_k^N, k = 0, 1,…,N are the coefficients of the N-length prediction-error filter, P_N is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).