<?xml version="1.0" encoding="UTF-8"?>
<!--
This file is part of the Scilab time frequency toolbox
This file must be used under the terms of the CeCILL.
This source file is licensed as described in the file COPYING, which
you should have received as part of this distribution.  The terms
are also available at
http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
-->

<refentry xml:id="tfrcw" 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:scilab="http://www.scilab.org"
          xmlns:ns3="http://www.w3.org/1999/xhtml"
          xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:db="http://docbook.org/ns/docbook">


  <refnamediv>
    <refname>tfrcw</refname>
	<refpurpose>Choi-Williams time-frequency distribution</refpurpose>
  </refnamediv>

<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   	[TFR,T,F] = tfrcw(X
   	[TFR,T,F] = tfrcw(X, T)
   	[TFR,T,F] = tfrcw(X, T, N)
   	[TFR,T,F] = tfrcw(X, T, N, G)
   	[TFR,T,F] = tfrcw(X, T, N, G, H)
   	[TFR,T,F] = tfrcw(X, T, N, G, H, SIGMA)
   	[TFR,T,F] = tfrcw(X, T, N, G, H, SIGMA)
   	[TFR,T,F] = tfrcw(...,'plot')
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
   <varlistentry>
     <term>X :</term>
     <listitem>
       <para> A Nx elements vector (auto-CW)  or a Nx by 2 array signal (cross-CW).</para>
     </listitem>
   </varlistentry>

   <varlistentry>
     <term> T:</term> 
     <listitem>
       <para>a real Nt vector with elements in [1 Nx] : time instant(s)
        (default: 1:NX).</para>
     </listitem>
   </varlistentry>

   <varlistentry>
     <term> N:</term> 
     <listitem><para> a positive integer: the number of frequency bins
     (default:NX). For faster computation N should be a power of
     2.</para>
   </listitem>
   </varlistentry>

   <varlistentry>
     <term> G:</term> 
     <listitem>
       <para> a real vector with odd length: the time smoothing
       window, (default :Hamming(N/10)).</para>
       <para>It will be normalized such as the middle point equals 1
       to preserve signal energy.</para>
   </listitem>
   </varlistentry>

   <varlistentry>
     <term> H :</term> 
     <listitem>
       <para> real vector with odd length: the frequency smoothing
       window,(default: Hamming(N/4)).</para>
       <para>It will be normalized such as the middle point equals 1
       to preserve signal energy.</para>
   </listitem>
   </varlistentry>
 
  <varlistentry>
     <term> SIGMA :</term> 
     <listitem>
       <para>a positive scalar: the kernel width (default : 1).</para>
   </listitem>
   </varlistentry>

   <varlistentry>
     <term> TRACE :</term> 
     <listitem>
       <para> A boolean (or a real scalar) if true (or nonzero),the progression of the algorithm is shown
       (default : %f).</para>
     </listitem>
   </varlistentry>

   <varlistentry>
     <term>'plot':</term> <listitem><para> if one input parameter is
     'plot', <link linkend="tfrqview">tfrqview</link> is called and
     the time-frequency representation will be plotted.</para>
     </listitem>
   </varlistentry>
   <varlistentry>
     <term> TFR :</term> 
     <listitem>
       <para> A real N by Nt array: the time-frequency representation.</para>
     </listitem>
   </varlistentry>
   <varlistentry>
     <term> F :</term> 
     <listitem>
       <para> A N vector of normalized frequencies.</para>
     </listitem>
   </varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
tfrcw computes the Choi-Williams distribution of a discrete-time
signal X, or the cross Choi-Williams representation between two
signals.
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <para> Interactive use </para>

   <programlisting role="example"><![CDATA[
N=128;
sig=fmlin(N,0.05,0.3)+fmlin(N,0.15,0.4);
g=window("kr",9,3*%pi); h=window("kr",27,3*%pi);
t=1:N; tfrcw(sig,t,N,g,h,3.6,1,'plot');
   ]]></programlisting>

 <para>Non interactive use</para>

   <programlisting role="example"><![CDATA[
N = 128;
sig = fmlin(N,0.05,0.3) + fmlin(N,0.15,0.4);
g = window("kr",9,3*%pi);
h = window("kr",27,3*%pi);
t = 1:N; 
[TFR,T,F] = tfrcw(sig,t,N,g,h,3.6);
clf; gcf().color_map = jetcolormap(128);
grayplot(T,F,TFR');
 ]]></programlisting>
  <scilab:image><![CDATA[
N = 128;
sig = fmlin(N,0.05,0.3) + fmlin(N,0.15,0.4);
g = window("kr",9,3*%pi);
h = window("kr",27,3*%pi);
t = 1:N; 
[TFR,T,F] = tfrcw(sig,t,N,g,h,3.6);
clf; gcf().color_map = jetcolormap(128);
grayplot(T,F,TFR');
    ]]></scilab:image>
</refsection>

<refsection>
   <title>Authors</title>
   <simplelist type="vert">
   <member>H. Nahrstaedt - Aug 2010</member>
   <member>	F. Auger, May-August 1994, July 1995.</member>
   <member>	Copyright (c) 1996 by CNRS (France).</member>
   </simplelist>
</refsection>
</refentry>
