<?xml version="1.0" encoding="UTF-8"?>
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 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
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 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
          xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
          xml:lang="en" xml:id="imrep2ss">
    <refnamediv>
        <refname>imrep2ss</refname>
        <refpurpose>state-space realization of an impulse response</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            sl = imrep2ss(v)
            sl = imrep2ss(v, deg)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>v</term>
                <listitem>
                    <para>
                        vector coefficients of impulse response, <literal>v(:,k)</literal> is the kth sample
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>deg</term>
                <listitem>
                    <para>integer (order required)</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>sl</term>
                <listitem>
                    <para>
                        <literal>syslin</literal> list
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Impulse response to linear system conversion (one input).
            <literal>v</literal> must have an even number of columns.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
s=poly(0,'s');
H=[1/(s+0.5);2/(s-0.4)]   //strictly proper
np=20;w=ldiv(H('num'),H('den'),np);
rep=[w(1:np)';w(np+1:2*np)'];   //The impulse response
H1=ss2tf(imrep2ss(rep))
z=poly(0,'z');
H=(2*z^2-3.4*z+1.5)/(z^2-1.6*z+0.8)     //Proper transfer function
u=zeros(1,20);u(1)=1;
rep=rtitr(H('num'),H('den'),u);   //Impulse rep.
//   <=> rep=ldiv(H('num'),H('den'),20)
w=z*imrep2ss(rep)   //Realization with shifted impulse response
// i.e strictly proper to proper
H2=ss2tf(w);
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="frep2tf">frep2tf</link>
            </member>
            <member>
                <link linkend="arl2">arl2</link>
            </member>
            <member>
                <link linkend="time_id">time_id</link>
            </member>
            <member>
                <link linkend="armax">armax</link>
            </member>
            <member>
                <link linkend="markp2ss">markp2ss</link>
            </member>
            <member>
                <link linkend="ldiv">ldiv</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
