Signal Processing/Lattice Predictors

Levinson-Durbin Algorithm
The Levinson-Durbin Algorithm is a direct method to solve the augmented Wiener-Hopf equations for the lattice predictor-error coefficients and the predictor-error power. The Levinson-Durbin algorithm uses the filter coefficients of an order m filter to compute the coefficients of an order m + 1 order filter.

There are two parts to the Levinson-Durbin Algorithm. The first part is a method to compute the tap-weight vector am using the tap-weight vector of a lower-order filter, am-1:


 * $$\mathbf{a}_m = \begin{bmatrix}\mathbf{a}_{m-1} \\ 0 \end{bmatrix} + \kappa_m \begin{bmatrix}0 \\ \mathbf{a}^{B*}_{m-1}\end{bmatrix}$$

In scalar form, this equation becomes:


 * $$a_{m,k} = a_{m-1,k-1} + \kappa_m a_{m-1,m-k}$$