# 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:

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

In scalar form, this equation becomes:

${\displaystyle a_{m,k}=a_{m-1,k-1}+\kappa _{m}a_{m-1,m-k}}$