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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from schurrc.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="schurrc" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>schurrc</refname>
<refpurpose>Computes reflection coefficients from auto-correlation sequence using Schrur algorithm.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
k = schurrc(r)
[k,e] = schurrc(r)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>k:</term>
<listitem><para> reflection coefficients or lattice parameters of prediction filter</para></listitem></varlistentry>
<varlistentry><term>e:</term>
<listitem><para> prediction error variance</para></listitem></varlistentry>
<varlistentry><term>r:</term>
<listitem><para>auto correltion sequence </para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>k = schurrc(r) uses the Schur algorithm to compute a vector k of reflection coefficients from a vector r representing an autocorrelation sequence. k and r are the same size. The reflection coefficients represent the lattice parameters of a prediction filter for a signal with the given autocorrelation sequence, r. When r is a matrix, schurrc treats each column of r as an independent autocorrelation sequence, and produces a matrix k, the same size as r. Each column of k represents the reflection coefficients for the lattice filter for predicting the process with the corresponding autocorrelation sequence r.</para>
<para>[k,e] = schurrc(r) also computes the scalar e, the prediction error variance. When r is a matrix, e is a column vector. The number of rows of e is the same as the number of columns of r.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
m=linspace(1,100);
r = xcorr(m(1:5),'unbiased');
[k,e] = schurrc(r(5:$))
//EXPECTED OUTPUT
//e =1.6212406
//k = - 0.9090909 0.2222222 0.2244898 0.2434211
]]></programlisting>
</refsection>
</refentry>
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