The Levinson-Durbin algorithm described in Section 12.4.1 solved the linear equations...

The Levinson-Durbin algorithm described in Section 12.4.1 solved the linear equations

where the right-hand side of this equation has elements of the autocorrelation sequence that are also elements of the matrix Let us consider the more general problem of solving the linear equations

where is an arbitrary vector. (The vector is not related to the coefficients of the backward predictor.) Show that the solution to can be obtained from a generalized Levinson-Durbin algorithm which is given recursively as