scilab/modules/signal_processing/help/en_US/correlation_convolution/conv.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_US" xml:id="conv">
   3     <refnamediv>
   4         <refname>conv</refname>
   5         <refpurpose>discrete 1-D convolution. </refpurpose>
   6     </refnamediv>
   7     <refsynopsisdiv>
   8         <title>Syntax</title>
   9         <synopsis>C = conv(A,B [,shape])</synopsis>
  10     </refsynopsisdiv>
  11     <refsection>
  12         <title>Parameters</title>
  13         <variablelist>
  14             <varlistentry>
  15                 <term>A</term>
  16                 <listitem>
  17                     <para>
  18                         a real or complex vector.
  19                     </para>
  20                 </listitem>
  21             </varlistentry>
  22             <varlistentry>
  23                 <term>B</term>
  24                 <listitem>
  25                     <para>
  26                         a real or complex vector.
  27                     </para>
  28                 </listitem>
  29             </varlistentry>
  30             <varlistentry>
  31                 <term>shape</term>
  32                 <listitem>
  33                     <para>
  34                         an optional character string with possible values:
  35                     </para>
  36                     <itemizedlist>
  37                         <listitem>
  38                             <literal>"full"</literal>, <literal>conv</literal>
  39                             computes the full convolution. It is the
  40                             default value.
  41                         </listitem>
  42                         <listitem>
  43                             <literal>"same"</literal>, <literal>conv</literal>
  44                             computes the central part of the convolution of the same
  45                             size as <literal>A</literal>.
  46                         </listitem>
  47                         <listitem>
  48                             <literal>"valid"</literal>, <literal>conv</literal>
  49                             computes the convolution parts without the zero-padding
  50                             of <literal>A</literal>.
  51                         </listitem>
  52                     </itemizedlist>
  53                 </listitem>
  54             </varlistentry>
  55             <varlistentry>
  56                 <term>C</term>
  57                 <listitem>
  58                     <para>
  59                         a real or complex vector.
  60                     </para>
  61                 </listitem>
  62             </varlistentry>
  63         </variablelist>
  64     </refsection>
  65     <refsection>
  66         <title>Description</title>
  67         <para>
  68             <literal>conv</literal> uses a straightforward formal
  69             implementation of the one-dimensional convolution equation in
  70             spatial form.
  71         </para>
  72         <para>
  73             <literal>C=conv(A,B [,shape])</literal> computes the
  74             one-dimensional convolution of the vectors <literal>A</literal>
  75             and <literal>B</literal>:
  76         </para>
  77         <itemizedlist>
  78             <listitem>
  79                 With <literal>shape=="full"</literal> the
  80                 dimensions of the result<literal>C</literal> are given by
  81                 <literal>size(A,'*')+size(B,'*')+1</literal>. The indices of the
  82                 center element of <literal>B</literal> are defined as
  83                 <literal>floor((size(B,'*')+1)/2)</literal>.
  84             </listitem>
  85             <listitem>
  86                 With <literal>shape=="same"</literal> the
  87                 dimensions of the result<literal>C</literal> are given by
  88                 <literal>size(A)</literal>. The indices of the
  89                 center element of <literal>B</literal> are defined as
  90                 <literal>floor((size(B,'*')+1)/2)</literal>.
  91             </listitem>
  92             <listitem>
  93                 With <literal>shape=="valid"</literal> the dimensions
  94                 of the result <literal>C</literal> are given by
  95                 <literal>size(A,'*')-size(B,'*')+1)</literal> if
  96                 <literal>and(size(A,'*')-size(B,'*'))&gt;=0</literal> else
  97                 <literal>C</literal> is empty . The indices of the center
  98                 element of <literal>B</literal> are defined as
  99                 <literal>1</literal>.
 100             </listitem>
 101         </itemizedlist>
 102         <para>
 103             Note that <link linkend="convol">convol</link> can be more efficient for large arrays.
 104         </para>
 105     </refsection>
 106     <refsection>
 107         <title>Examples</title>
 108         <programlisting role="example"><![CDATA[
 109         A=1:10;
 110         B=[1 -1];
 111         conv(A,B)
 112     ]]></programlisting>
 113     </refsection>
 114     <refsection role="see also">
 115         <title>See also</title>
 116         <simplelist type="inline">
 117             <member>
 118                 <link linkend="convol">convol</link>
 119             </member>
 120             <member>
 121                 <link linkend="conv2">conv2</link>
 122             </member>
 123         </simplelist>
 124     </refsection>
 125     <refsection>
 126         <title>Used Functions</title>
 127         <para>
 128             The conv function is based on the  <link linkend="conv2">conv2</link> builtin.
 129         </para>
 130     </refsection>
 131     <refsection>
 132         <title>History</title>
 133         <revhistory>
 134             <revision>
 135                 <revnumber>5.4.0</revnumber>
 136                 <revremark>Function conv introduced.</revremark>
 137             </revision>
 138         </revhistory>
 139     </refsection>
 140 </refentry>