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  <refnamediv>
    <refname>hilbert1</refname>
    <refpurpose>Compute the analytic extension of a real-valued signal.</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Syntax</title>
   <synopsis>
   h = hilbert1(f)
   h = hilbert1(f, N)
   h = hilbert1(f, N, dim)
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
        <varlistentry>
            <term>f :</term>
            <listitem><para> real-valued input signal. Can be a vector, matrix, or N-D array.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>N :</term>
            <listitem><para> (optional) length of the Hilbert transform. Must be a positive integer.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>dim :</term>
            <listitem><para> (optional) dimension along which the Hilbert transform is applied. Must be a scalar.</para></listitem>
        </varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
Compute the analytic extension of a real-valued signal.
   </para>
   <para>
- h = hilbert1(f) computes the analytic signal of the real-valued input signal f.
If f is a matrix, the transformation is applied to each column. For N-D arrays,
the transformation is applied to the first non-singleton dimension.
- real(h) contains the original signal f.
- imag(h) contains the Hilbert transform of f.
- hilbert1(f, N) computes the Hilbert transform with a length N. The result will also have length N.
- hilbert1(f, [], dim) or hilbert1(f, N, dim) applies the transformation along the specified dimension.
   </para>
   <para>
</para>
</refsection>

<refsection role="see also">
   <title>See also</title>
   <simplelist type="inline">
   <member><link linkend="fft1">fft1</link></member>
   <member><link linkend="ifft1">ifft1</link></member>
   <member><link linkend="ipermute">ipermute</link></member>
   </simplelist>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
// The magnitude of the Hilbert transform eliminates the carrier
t = linspace(0, 10, 1024);
x = 5 * cos(0.2 * t) .* sin(100 * t);
plot(t, x, t, abs(hilbert1(x)));
   ]]></programlisting>
</refsection>
</refentry>
