THE BURG METHOD
The standard direct-form FIR filter can be implemented in a lattice structure:


The reflection coefficients can be computed directly using this equation:


For this filter to be stable, the reflection coefficients must be bounded by 1.

This equation represents one solution from a family of solutions based on lattice methods.

One of the most famous lattice formulations in this family is the Burg algorithm, originally introduced in the mid-60's prior to the introduction of LP in speech. There are actually a family of lattice solutions of a similar form. The Burg algorithm requires the coefficients to be computed using:


We see this is a weighted average of the forward and backward error terms, and that the reflection coefficients are FORCED to be bounded.