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:

${𝐚}_m=\left[\begin{array}{c}{𝐚}_{m-1}\\ 0\end{array}\right]+{\kappa }_m\left[\begin{array}{c}0\\ {𝐚}_{m-1}^{B*}\end{array}\right]$

In scalar form, this equation becomes:

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