code changes by Shashikiran Yadalam during FOSSEE Fellowship 2018

1 files changed, 104 insertions, 5 deletions

diff --git a/help/en_US/rlevinson.xml b/help/en_US/rlevinson.xml
index 799fcb1..5017af8 100644
--- a/help/en_US/rlevinson.xml
+++ b/help/en_US/rlevinson.xml
@@ -17,17 +17,116 @@
 
   <refnamediv>
     <refname>rlevinson</refname>
-    <refpurpose></refpurpose>
+    <refpurpose>This function computes the autocorrelation coefficients using prediction polynomial method.</refpurpose>
   </refnamediv>
 
 
 <refsynopsisdiv>
    <title>Calling Sequence</title>
    <synopsis>
-   a = rlevinson(a, efinal)
-   [a, U] = rlevinson(a, efinal)
-   [a, U, kr] = rlevinson(a, efinal)
-   [a, U, kr, e] = rlevinson(a, efinal)
+   R = rlevinson(a, efinal)
+   [R, U] = rlevinson(a, efinal)
+   [R, U, kr] = rlevinson(a, efinal)
+   [R, 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>