文档介绍：Problem: Show that the Wiener-Hopf equation, defining the tap-weight vector w o of the Wiener filter, and the equation defining the minimum mean-squared error J min may bined into a single matrix relation The matrix A is the correlation matrix of the augmented vector where d(n) is the desired response and u(n) is the tap-input vector of the Wiener filter. Key : The optimum filtering solution is defined by the Wiener-Hopf equation Rw o=p( 1) for which the minimum mean-square error equals (2) Combine Eqs. (1) and (2) into a single relation: Define ( 3) Since , and we may rewrite Eq. (3) as The minimum mean-square error equals (4) Eliminate between Eqs. (1) and (4): where we have used the property We may rewrite Eq. (6) simply as which clearly show that J(w o)=J min .