Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If SE(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 SL(f,M) is given by
1SL(f,M)=1Mj=0M11SE(f,j).
The maximum entropy estimates are made via Burg's well-known formula,
SE(f,N)=PNΔt|k=0NγkNei2πfkΔt|2,
where γkN, k = 0, 1,…,N are the coefficients of the N-length prediction-error filter, PN is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).
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