User`s guide

Levinson-Durbin
5-264
5Levinson-Durbin
Purpose Solve a linear system of equations using Levinson-Durbin recursion.
Library Math Functions / Matrices and Linear Algebra / Linear System Solvers
Description The Levinson-Durbin block solves the nth-order system of linear equations
for the particular case where R is a Hermitian, positive-definite, Toeplitz
matrix and b is identical to the first column of R shifted by one element and
with the opposite sign.
The input to the block,
r = [r(1) r(2) ... r(n+1)], can be a 1-D or 2-D
vector (row or column). It contains lags 0 through n of an autocorrelation
sequence, which appear in the matrix R.
The block can output the polynomial coefficients, A, the reflection
coefficients, K, and the prediction error power, P, in various combinations. The
Output(s) parameter allows you to enable the A and K outputs by selecting one
of the following settings:
•
A – Port A outputs A=[1 a(2) a(3) ... a(n+1)], the solution to the
Levinson-Durbin equation. A has the same dimension as the input. The
elements of the output can also be viewed as the coefficients of an nth-order
autoregressive (AR) process (see below).
•
K – Port K outputs K=[k(1) k(2) ... k(n)], which contains n reflection
coefficients, and has the same dimension as the input, less one element.
(A scalar input causes an error when
K is selected.) Reflection coefficients
are useful for realizing a lattice representation of the AR process described
below.
•
A and K – The block outputs both representations at their respective ports.
(A scalar input causes an error when
AandK is selected.)
Both A and K are always 1-D vectors.
Ra b=
r 1() r
*
2() L r
*
n()
r 2() r 1() L r
*
n 1–()
MMOM
rn()rn 1–()L r 1()
a 2()
a 3()
M
a n 1+()
r 2()–
r 3()–
M
rn 1+()–
=