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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/cacsd/help/en_US/format_representation/frep2tf.xml
 
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<?xml version="1.0" encoding="UTF-8"?>
 
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<!--
 
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 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 
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 * Copyright (C) INRIA - 
 
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 * 
 
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 * This file must be used under the terms of the CeCILL.
 
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 * This source file is licensed as described in the file COPYING, which
 
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 * you should have received as part of this distribution.  The terms
 
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 * are also available at    
 
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 * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
 
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 *
 
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 -->
 
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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" version="5.0-subset Scilab" xml:lang="en" xml:id="frep2tf">
 
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    <refnamediv>
 
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        <refname>frep2tf</refname>
 
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        <refpurpose> transfer function realization from frequency response</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[h [,err]]=frep2tf(frq,repf,dg [,dom,tols,weight])</synopsis>
 
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    </refsynopsisdiv>
 
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    <refsection>
 
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        <title>Arguments</title>
 
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        <variablelist>
 
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            <varlistentry>
 
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                <term>frq</term>
 
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                <listitem>
 
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                    <para>vector of frequencies in Hz.</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>repf</term>
 
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                <listitem>
 
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                    <para>vector of frequency response</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>dg</term>
 
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                <listitem>
 
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                    <para>degree of linear system</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>dom</term>
 
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                <listitem>
 
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                    <para>
 
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                        time domain (<literal>'c'</literal> or <literal>'d'</literal> or <literal>dt</literal>)
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>tols</term>
 
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                <listitem>
 
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                    <para>
 
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                        a vector of size 3 giving the relative and absolute tolerance  and the maximum number of iterations (default values are <literal>rtol=1.e-2; atol=1.e-4, N=10</literal>).
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>weight</term>
 
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                <listitem>
 
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                    <para>vector of weights on frequencies</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>h</term>
 
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                <listitem>
 
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                    <para>SISO transfer function</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>err</term>
 
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                <listitem>
 
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                    <para>
 
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                        error (for example if <literal>dom='c'</literal> <literal>sum(abs(h(2i*pi*frq) - rep)^2)/size(frq,*)</literal>)
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Description</title>
 
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        <para>
 
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            Frequency response to  transfer function conversion. The order of <literal>h</literal>
 
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            is a priori given in <literal>dg</literal> which must be provided.
 
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            The following linear system is solved in the least square sense.
 
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        </para>
 
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        <programlisting role=""><![CDATA[ 
 
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 weight(k)*(n( phi_k) - d(phi_k)*rep_k)=0, k=1,..,n
 
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 ]]></programlisting>
 
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        <para>
 
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            where <literal>phi_k= 2*%i*%pi*frq</literal> when <literal>dom='c'</literal> and <literal>phi_k=exp(2*%i*%pi*dom*frq</literal> if not. If the <literal>weight</literal> vector is not given a default 
 
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            penalization is used (when <literal>dom='c'</literal>).
 
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        </para>
 
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        <para>
 
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            A stable and minimum phase system can be obtained by using function <literal>factors</literal>.
 
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        </para>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Examples</title>
 
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        <programlisting role="example"><![CDATA[ 
 
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s=poly(0,'s');
 
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h=syslin('c',(s-1)/(s^3+5*s+20))
 
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frq=0:0.05:3;repf=repfreq(h,frq);
 
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clean(frep2tf(frq,repf,3))
 
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Sys=ssrand(1,1,10); 
 
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frq=logspace(-3,2,200);
 
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[frq,rep]=repfreq(Sys,frq);  //Frequency response of Sys
 
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[Sys2,err]=frep2tf(frq,rep,10);Sys2=clean(Sys2)//Sys2 obtained from freq. resp of Sys
 
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[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
 
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clf();bode(frq,[rep;rep2])   //Responses of Sys and Sys2
 
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[gsort(spec(Sys('A'))),gsort(roots(Sys2('den')))] //poles
 
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dom=1/1000; // Sampling time 
 
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z=poly(0,'z');
 
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h=syslin(dom,(z^2+0.5)/(z^3+0.1*z^2-0.5*z+0.08))
 
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frq=(0:0.01:0.5)/dom;repf=repfreq(h,frq);
 
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[Sys2,err]=frep2tf(frq,repf,3,dom);
 
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[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
 
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clf();plot2d1("onn",frq',abs([repf;rep2])');
 
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]]></programlisting>
 
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    </refsection>
 
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    <refsection role="see also">
 
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        <title>See Also</title>
 
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        <simplelist type="inline">
 
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            <member>
 
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                <link linkend="imrep2ss">imrep2ss</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="arl2">arl2</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="time_id">time_id</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="armax">armax</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="frfit">frfit</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
 
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</refentry>