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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from corrmtx.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="corrmtx" 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>corrmtx</refname>
<refpurpose>Generate data matrix for autocorrelation matrix estimation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
X = corrmtx(x,m)
[X,R] = corrmtx(x,m)
X = corrmtx(x,m,s)
[X,R] = corrmtx(x,m,s)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>x:</term>
<listitem><para> input vector of size N for which correlation matrix of size m is to be calculated</para></listitem></varlistentry>
<varlistentry><term>m:</term>
<listitem><para> size of correlation matrix to be computed. Positive integer strictly smaller than the length of the input x</para></listitem></varlistentry>
<varlistentry><term>X:</term>
<listitem><para> data matrix as specified according to the input 'method'</para></listitem></varlistentry>
<varlistentry><term>s:</term>
<listitem><para> method for type of output matrix X</para></listitem></varlistentry>
<varlistentry><term>'autocorrelation':</term>
<listitem><para> (default) X is the (n + m)-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the leng th-n data vector x, derived using prewindowed and postwindowed data, based on an mth-order prediction error model.</para></listitem></varlistentry>
<varlistentry><term>'prewindowed':</term>
<listitem><para> X is the n-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n data vector x, derived using prewindowed data, based on an mth-order prediction error model.</para></listitem></varlistentry>
<varlistentry><term>'postwindowed':</term>
<listitem><para> X is the n-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n data vector x , derived using postwindowed data, based on an mth-order prediction error model.</para></listitem></varlistentry>
<varlistentry><term>'covariance':</term>
<listitem><para> X is the (n – m)-by-(m + 1) rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n data vect or x, derived using nonwindowed data, based on an mth-order prediction error model.</para></listitem></varlistentry>
<varlistentry><term>'modified':</term>
<listitem><para> X is the 2(n – m)-by-(m + 1) modified rectangular Toeplitz matrix that generates an autocorrelation estimate for the length-n d ata vector x, derived using forward and backward prediction error estimates, based on an mth-order prediction error model.</para></listitem></varlistentry>
<varlistentry><term>R:</term>
<listitem><para> (m + 1)-by-(m + 1) autocorrelation matrix estimate calculated as X'*X</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Consider the generic matrix X below
_ _
| x(1) ..........0 |
| : . : |
| : . : |
| x(m+1).......x(1)|
| : . : |
| : . : |
X = | x(n-m).....x(m+1)|
| : . : |
| : . : |
| x(n).......x(n-m)|
| : . : |
| : . : |
|_0 ..........x(n)_|
--
For different inputs of string s the output would vary ass described below
'autocorrelation' — (default) X = X, above.
'prewindowed' — X is the n-by-(m + 1) submatrix of X whose first row is [x(1) … 0] and whose last row is [x(n) … x(n – m)]
'postwindowed' — X is the n-by-(m + 1) submatrix of X whose first row is [x(m + 1) … x(1)] and whose last row is [0 … x(n)]
'covariance' — X is the (n – m)-by-(m + 1) submatrix of X whose first row is [x(m + 1) … x(1)] and whose last row is [x(n) … x(n – m)]
'modified' — X is the 2(n – m)-by-(m + 1) matrix X_mod shown below
_ _
| x(m+1) ......x(1)|
| : . : |
| : . : |
| x(n-m).....x(m+1)|
| : . : |
| : . : |
| x(n).......x(n-m)|
X_mod= | x*(1).....x*(m+1)|
| : . : |
| : . : |
| x*(m+1)...x*(n-m)|
| : . : |
| : . : |
|_x*(n-m) ...x*(n)_|
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
]]></programlisting>
</refsection>
<refsection>
<title>See also</title>
<simplelist type="inline">
<member><link linkend="peig">peig</link></member>
<member><link linkend="pmusic">pmusic</link></member>
<member><link linkend="rooteig">rooteig</link></member>
<member><link linkend="rootmusic">rootmusic</link></member>
<member><link linkend="xcorr">xcorr</link></member>
<member><link linkend="Author:">Author:</link></member>
<member><link linkend="Parthe">Pandit</link></member>
<member><link linkend="Bilbligraphy">Bilbligraphy</link></member>
<member><link linkend="Marple,">S. Lawrence. Digital Spectral Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1987.</link></member>
</simplelist>
</refsection>
</refentry>
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