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We derive the method of maximum entropy spectrum estimation by bordering techniques of linear algebra. Using bordering, we obtain the recursive solution to the Yule-Walker equations and the recursive equation for the Toeplitz determinant in terms of the partial correlation coefficients. Minimization of the forward and backward predictor errors is then done with respect to the partial correlation coefficients. The minimization is done stagewise, constraining higher partial correlation values to zero. Thus, the minimization is done for a maximum-entropy normal process; the Toeplitz determinant is a maximum.
Date of Publication: Jan 1983