Typo fixes
[scilab.git] / scilab / modules / signal_processing / help / en_US / hilbert.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <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" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="hilbert">
3     <refnamediv>
4         <refname>hilbert</refname>
5         <refpurpose>Discrete-time analytic signal computation of a real signal  using Hilbert transform </refpurpose>
6     </refnamediv>
7     <refsynopsisdiv>
8         <title>Syntax</title>
9         <synopsis>x=hilbert(xr)</synopsis>
10     </refsynopsisdiv>
11     <refsection>
12         <title>Arguments</title>
13         <variablelist>
14             <varlistentry>
15                 <term>xr</term>
16                 <listitem>
17                     <para>real vector : the real signal samples</para>
18                 </listitem>
19             </varlistentry>
20             <varlistentry>
21                 <term>x</term>
22                 <listitem>
23                     <para>Complex vector: the discrete-time analytic signal.</para>
24                 </listitem>
25             </varlistentry>
26         </variablelist>
27     </refsection>
28     <refsection>
29         <title>Description</title>
30         <para>Returns theanalytic signal, from a real data sequence.</para>
31         <para>
32             The analytic signal <literal>x= xr + i*xi</literal> has a real part, <literal>xr</literal>, which
33             is the original data, and an imaginary part, <literal>xi</literal>, which contains
34             the Hilbert transform. The imaginary part is a version of the
35             original real sequence with a 90° phase shift.
36         </para>
37     </refsection>
38     <refsection>
39         <title>References</title>
40         <para>
41             <literal>
42                 <ulink url="http://ieeexplore.ieee.org/iel5/78/16975/00782222.pdf?arnumber=782222">http://ieeexplore.ieee.org/iel5/78/16975/00782222.pdf?arnumber=782222</ulink>
43             </literal>
44         </para>
45         <para>
46             Marple, S.L., "Computing the discrete-time analytic signal via FFT,"
47             IEEE Transactions on Signal Processing, Vol. 47, No.9 (September
48             1999), pp.2600-2603
49         </para>
50     </refsection>
51     <refsection role="see also">
52         <title>See Also</title>
53         <simplelist type="inline">
54             <member>
55                 <link linkend="window">window</link>
56             </member>
57             <member>
58                 <link linkend="hilb">hil</link>
59             </member>
60         </simplelist>
61     </refsection>
62     <refsection>
63         <title>Examples</title>
64         <programlisting role="example"><![CDATA[ 
65 //compare the discrete-time analytic signal imaginary part of the impulse real signal 
66 // with the FIR approximation of the Hilbert transform filter
67 m=25;
68 n=2*m+1;
69 y=hilbert(eye(n,1));
70 h=hilb(n)';
71 h=[h((m+1):$);h(1:m)];
72 plot([imag(y) h])
73  ]]></programlisting>
74         <scilab:image>
75             m=25;
76             n=2*m+1;
77             y=hilbert(eye(n,1));
78             h=hilb(n)';
79             h=[h((m+1):$);h(1:m)];
80             plot([imag(y) h])
81         </scilab:image>
82     </refsection>
83 </refentry>