diff options
Diffstat (limited to 'help/en_US/rlevinson.xml')
-rw-r--r-- | help/en_US/rlevinson.xml | 109 |
1 files changed, 5 insertions, 104 deletions
diff --git a/help/en_US/rlevinson.xml b/help/en_US/rlevinson.xml index 5017af8..799fcb1 100644 --- a/help/en_US/rlevinson.xml +++ b/help/en_US/rlevinson.xml @@ -17,116 +17,17 @@ <refnamediv> <refname>rlevinson</refname> - <refpurpose>This function computes the autocorrelation coefficients using prediction polynomial method.</refpurpose> + <refpurpose></refpurpose> </refnamediv> <refsynopsisdiv> <title>Calling Sequence</title> <synopsis> - R = rlevinson(a, efinal) - [R, U] = rlevinson(a, efinal) - [R, U, kr] = rlevinson(a, efinal) - [R, U, kr, e] = rlevinson(a, efinal) + a = rlevinson(a, efinal) + [a, U] = rlevinson(a, efinal) + [a, U, kr] = rlevinson(a, efinal) + [a, U, kr, e] = rlevinson(a, efinal) </synopsis> </refsynopsisdiv> - -<refsection> - <title>Parameters</title> - <variablelist> - <varlistentry><term>a:</term> - <listitem><para>Input argument ,prediction polynomial coefficients.</para></listitem></varlistentry> - <varlistentry><term>efinal:</term> - <listitem><para>Input argument, final prediction error.</para></listitem></varlistentry> - <varlistentry><term>R:</term> - <listitem><para>Returns the auto-correlation coefficients.</para></listitem></varlistentry> - -<varlistentry><term>U:</term> - <listitem><para>Returns upper triangular matrix of order length(a)*length(a).</para></listitem></varlistentry> - <varlistentry><term>kr:</term> - <listitem><para>Reflection coefficients.</para></listitem></varlistentry> - -<varlistentry><term>e:</term> - <listitem><para>Prediction error.</para></listitem></varlistentry> - </variablelist> - -</refsection> - -<refsection> - <title>Description - </title> -<para>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).</para> -<para> -<latex> -\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} - -</latex> -</para> - -<para> -Input vector a represents the polynomial coefficients of this prediction error filter in descending powers of z. -<para> -<latex> -\begin{eqnarray} -A(z)=1+a(2)^{z-1}+.............+a(n+1)^{z-p} -\end{eqnarray} -</latex></para> -</para> -<para>[r,u] = rlevinson(a,efinal) returns upper triangular matrix U from the UDU* decomposition - -</para> -<latex> -\begin{eqnarray} -R^{-1}=UE^{-1}U* -\end{eqnarray} -</latex> -<para> -<latex> - -</latex> -</para> -</refsection> - -<refsection> - <title>Examples</title> - <programlisting role="example"><![CDATA[ -X=[1 6/7 5/7 8/7 3/7 6/7]; -[R U kr e] = rlevinson(X, 0.3) - ]]></programlisting> -</refsection> - -<refsection> - <title>See also</title> - <simplelist type="inline"> - <member><link linkend="levinson">abs</link></member> - <member><link linkend="levdown">mean</link></member> - - </simplelist> -</refsection> - - - </refentry> |