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<refentry xml:id="fmhyp" xml:lang="en"
          xmlns="http://docbook.org/ns/docbook"
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          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>fmhyp</refname>
	<refpurpose>Signal with hyperbolic frequency modulation</refpurpose>
  </refnamediv>

  <refsynopsisdiv>
    <title>Calling Sequence</title>
    <synopsis>
      [X,IFLAW] = fmhyp(N, P1, P2)
    </synopsis>
  </refsynopsisdiv>

  <refsection>
    <title>Parameters</title>
    <variablelist>
      <varlistentry>
        <term>N  :</term>
        <listitem>
          <para>a positive integer:  number of points in time</para>
        </listitem>
      </varlistentry>
      <varlistentry>
        <term>P1 :</term>
        <listitem>
          <para>a real 2 elements vector:</para>
          <para> if the number of input arguments is 2, P1 is a vector
          containing the two coefficients [F0 C] for an hyperbolic
          instantaneous frequency .</para>

          <para> if the number of input arguments is 3, P1 is a
          time-frequency point of the form [t,f]. where t is in
          seconds and f is a normalized frequency (between 0 and
          0.5). </para>
        </listitem>
      </varlistentry>
      <varlistentry>
        <term>P2 :</term>
        <listitem>
          <para>a real 2 elements vector:</para>
          <para>P2 is a time-frequency point of the form [t,f]. where
          t is in seconds and f is a normalized frequency (between 0
          and 0.5). </para>
        </listitem>
      </varlistentry>
      <varlistentry>
        <term>X  :</term>
        <listitem>
          <para> real column vector: the modulated signal time
          samples. Sampling frequency is set to 1.</para>
        </listitem>
      </varlistentry>
      <varlistentry>
        <term>IFLAW :</term>
        <listitem>
          <para>real column vector: instantaneous frequency law</para>
        </listitem>
      </varlistentry>
    </variablelist>
  </refsection>

  <refsection>
    <title>Description</title>
    <para>
      fmhyp generates a signal with hyperbolic frequency modulation :
      X(t) = exp(i.2.pi(F0.t + C/log|t|)).  When called with 3 input
      arguments F0 and C are derived from P1 and P2 such that the
      frequency modulation law fits the points P1 and P2.
    </para>
  </refsection>

  <refsection>
    <title>Examples</title>
    <programlisting role="example"><![CDATA[
    [X,IFLAW] = fmhyp(128,[1 .5],[32 0.1]);
    clf
    subplot(211); plot(real(X)); xtitle(_("Signal real part"))
    subplot(212); plot(IFLAW); xtitle(_("Instantaneous frequency law"))
    ]]></programlisting>
    <scilab:image><![CDATA[
    [X,IFLAW]=fmhyp(128,[1 .5],[32 0.1]);
    clf;
    subplot(211); plot(real(X));xtitle(_("Signal real part"))
    subplot(212); plot(IFLAW);xtitle(_("Instantaneous frequency law"))
    ]]></scilab:image>
  </refsection>

  <refsection role="see also">
    <title>See also</title>
    <simplelist type="inline">
      <member><link linkend="fmlin">fmlin</link></member>
      <member><link linkend="fmsin">fmsin</link></member>
      <member><link linkend="fmpar">fmpar</link></member>
      <member><link linkend="fmconst">fmconst</link></member>
      <member><link linkend="fmodany">fmodany</link></member>
      <member><link linkend="fmpower">fmpower</link></member>
    </simplelist>
  </refsection>

  <refsection>
    <title>Authors</title>
    <simplelist type="vert">
      <member>H. Nahrstaedt - Aug 2010</member>
      <member>P. Goncalves - October 1995, O. Lemoine - November 1995</member>
    </simplelist>
  </refsection>
</refentry>
