rlevinson
This function computes the autocorrelation coefficients using prediction polynomial method.
Calling Sequence
R = rlevinson(a, efinal)
[R, U] = rlevinson(a, efinal)
[R, U, kr] = rlevinson(a, efinal)
[R, U, kr, e] = rlevinson(a, efinal)
Parameters
a:
Input argument ,prediction polynomial coefficients.
efinal:
Input argument, final prediction error.
R:
Returns the auto-correlation coefficients.
U:
Returns upper triangular matrix of order length(a)*length(a).
kr:
Reflection coefficients.
e:
Prediction error.
Description
The reverse Levinson-Durbin recursion implements the step-down algorithm for solving the following symmetric Toeplitz system of linear equations for r, where r = [r(1) … r(p + 1)] and r(i)* denotes the complex conjugate of r(i).
\begin{eqnarray}
\begin{bmatrix}
r(1) r(2)* - - r(p)* \\
r(2) r(1) - - r(p-1)* \\
- - - - - \\
- - - - - \\
- - - - - \\
r(p) r(p-1) - r(2) r(1)
\end{bmatrix}\begin{bmatrix}
a(2)\\
a(3)\\
.\\
.\\
.\\
a(p+1)
\end{bmatrix}=\begin{bmatrix}
-r(2)\\
-r(3)\\
.\\
.\\
.\\
-r(p+1)
\end{bmatrix}
\end{eqnarray}
Input vector a represents the polynomial coefficients of this prediction error filter in descending powers of z.
\begin{eqnarray}
A(z)=1+a(2)^{z-1}+.............+a(n+1)^{z-p}
\end{eqnarray}
[r,u] = rlevinson(a,efinal) returns upper triangular matrix U from the UDU* decomposition
\begin{eqnarray}
R^{-1}=UE^{-1}U*
\end{eqnarray}
Examples
See also
abs
mean