# predic - a j 1 = 1 a j[1 a j[2 a j j Γ j 1 a j j a j j-1 a...

This preview shows page 1. Sign up to view the full content.

Overview of Linear Prediction The Lenvinson-Durbin algorithm is a recursive solution to the symmetric–Toeplitz system of equations: R ( j ) x a j = ² j u 1 . that arises in the context of the linear prediction or the AR-modeling problem: ˆ x [ n ] = p X k =1 a p [ k ] x [ n - k ] e [ n ] = x [ n ] - p X k =1 a p [ k ] x [ n - k ] R xx [ l ] = p X k =1 a p [ k ] R xx [ l - k ] , l = 1 , 2 ,p ² p = R xx [0] + p X k =1 a p [ k ] R xx [ k ] . Levinson Durbin Recursion 1. Intialization: ² o = R xx [0], a 0 [0] = 1. 2. Reﬂection coeﬃcient for next stage: γ j = R xx [ j + 1] + j X k =1 a j [ k ] R xx [ j + 1 - k ] Γ j +1 = - γ j ² j . 3. Coeﬃcient update:
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a j +1 = 1 a j [1] a j [2] . . . a j [ j ] + Γ j +1 a j [ j ] a j [ j-1] . . . a j [1] 1 4. Modeling error update: ² j +1 = ² j ( 1-Γ 2 j +1 ) . 5. Go back to reﬂection coeﬃcent update. 1...
View Full Document

## This note was uploaded on 12/02/2011 for the course AR 107 taught by Professor Gracegraham during the Fall '11 term at Montgomery College.

Ask a homework question - tutors are online