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We derive a fast algorithm for calculating the Capon maximum likelihood method (MLM) power spectrum estimate when given uniformly spaced samples of the correlation function. This algorithm computes a weighted correlation of the predictor coefficients found by running Levinson recursion. The Fourier transform of the result gives the MLM spectrum. This approach also suggests an interesting new comparison between MLM and MEM.
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Bruce R. Musicus (1985) studied this question.
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