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 a_m using the tap-weight vector of a lower-order filter, a_m-1:

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

In scalar form, this equation becomes:

a_m,k = a_{m − 1,k − 1} + κ_ma_{m − 1,m − k}