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<refentry xml:id="tfrspbk" xml:lang="en"
          xmlns="http://docbook.org/ns/docbook"
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          xmlns:db="http://docbook.org/ns/docbook">

  <refnamediv>
    <refname>tfrspbk</refname><refpurpose>Smoothed Pseudo K-Bertrand
    time-frequency distribution.</refpurpose>
  </refnamediv>

<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   	[TFR,T,F] = tfrspbk(X)
   	[TFR,T,F] = tfrspbk(X, T)
   	[TFR,T,F] = tfrspbk(X, T, K)
   	[TFR,T,F] = tfrspbk(X, T, K, NH0)
   	[TFR,T,F] = tfrspbk(X, T, K, NH0,NG0)
   	[TFR,T,F] = tfrspbk(X, T, K, NH0,NG0, FMIN,FMAX)
   	[TFR,T,F] = tfrspbk(X, T, K, NH0,NG0, FMIN,FMAX, N)
   	[TFR,T,F] = tfrspbk(X, T, K, NH0,NG0, FMIN,FMAX, N, TRACE)
   	[TFR,T,F] = tfrspbk(...,'plot')
   </synopsis>
</refsynopsisdiv>

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

    <varlistentry>
      <term> T:</term> 
      <listitem>
        <para> a real Nt vector : time instant(s) (default: 1:NX).</para>
        <para>T must be a uniformly sampled vector whose elements are
        between 1 and Nx</para>
      </listitem>
    </varlistentry>

    
    <varlistentry>
      <term> K :</term> 
      <listitem>
        <para> label of the K-Bertrand distribution. The distribution
        with parametrization function lambdak(u,K) = (K
        (exp(-u)-1)/(exp(-Ku)-1))^(1/(K-1)) is computed (default :
        0).</para>
        <para> K=-1 : Smoothed pseudo (active) Unterberger distribution</para>
        <para> K=0 : Smoothed pseudo  Bertrand distribution</para>
        <para> K=0.5 : Smoothed pseudo D-Flandrin distribution</para>
        <para> K=2 :  Affine smoothed pseudo Wigner-Ville distribution</para>
      </listitem>
    </varlistentry>
    
    <varlistentry>
      <term> NH0 :</term> 
      <listitem>
        <para> half length of
        the analyzing wavelet at coarsest scale.  A Morlet wavelet is
        used. NH0 controles the frequency smoothing of the smoothed pseudo
        K-Bertrand distribution.(default :
        sqrt(Nx)).</para>
      </listitem>
    </varlistentry>

    <varlistentry>
      <term> NG0 :</term> 
      <listitem>
        <para> half length of the time smoothing window.  NG0 = 0
        corresponds to the Pseudo K-Bertrand distribution.  (default :
        0).</para>
      </listitem>
    </varlistentry>

    <varlistentry>
        <term> FMIN:</term> 
        <listitem>
          <para>
            a positive scalar in ]0 0.5], the normalized lower
            frequency bound in (Hz) of the analyzed signal. When
            unspecified, you have to enter it at the command line from
          the plot of the spectrum. </para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term> FMAX :</term> 
        <listitem>
          <para> a positive scalar in ]0 0.5], the normalized upper
          frequency bound (in Hz) of the analyzed signal.  When
          unspecified, you have to enter it at the command line from
          the plot of the spectrum.
          </para>
        </listitem>
      </varlistentry>
 
    <varlistentry>
      <term> N :</term> 
      <listitem><para>positive integer: the number of analyzed voices. When
          unspecified, you have to enter it at the command line from
          the plot of the spectrum.</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 complex N by Nt array: the time-frequency representation.</para>
        <para> abscissa correspond to uniformly sampled time, and
        ordinates correspond to a geometrically sampled
        frequency). First row of TFR corresponds to the lowest
        frequency.</para>
      </listitem>
    </varlistentry>

    <varlistentry>
      <term> F :</term> 
      <listitem>
        <para> A N vector of normalized frequencies (geometrically
        sampled from FMIN to FMAX).</para>
      </listitem>
    </varlistentry>
  </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
tfrspbk generates the auto or cross Smoothed Pseudo K-Bertrand
distribution.
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
N = 64,
sig = altes(N,0.1,0.45); 
[TFR,T,F] = tfrspbk(sig,1:N,0,sqrt(N),0,0.1,0.35,8);
clf; gcf().color_map = jetcolormap(128);
Sgrayplot(T,F,TFR');
   ]]></programlisting>
  <scilab:image><![CDATA[
N = 64,
sig = altes(N,0.1,0.45); 
[TFR,T,F] = tfrspbk(sig,1:N,0,sqrt(N),0,0.1,0.35,8);
clf; gcf().color_map = jetcolormap(128);
Sgrayplot(T,F,TFR');
    ]]></scilab:image>
</refsection>

<refsection>
   <title>Authors</title>
   <simplelist type="vert">
   <member>H. Nahrstaedt - Aug 2010</member>
   <member>	P. Goncalves, October 95 - O. Lemoine, June 1996.</member>
   <member>	Copyright (c) 1995 Rice University</member>
   </simplelist>
</refsection>
</refentry>
