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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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Lines of Context:
modules/signal_processing/help/ja_JP/xcorr.xml
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http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
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-->
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="xcorr" xml:lang="ja">
12
 
  <refnamediv>
13
 
    <refname>xcorr</refname>
14
 
    <refpurpose>離散自己/相互相関を計算する</refpurpose>
15
 
  </refnamediv>
16
 
  <refsynopsisdiv>
17
 
    <title>呼び出し手順</title>
18
 
    <synopsis>[c [,lagindex]] = xcorr(x [,maxlags [,scaling]])
19
 
      [c [,lagindex]] = xcorr(x,y [,maxlags [,scaling]])
20
 
    </synopsis>
21
 
  </refsynopsisdiv>
22
 
  <refsection>
23
 
    <title>パラメータ</title>
24
 
    <variablelist>
25
 
      <varlistentry>
26
 
        <term>x</term>
27
 
        <listitem>
28
 
          <para>実数または複素浮動小数点数のベクトル.</para>
29
 
        </listitem>
30
 
      </varlistentry>
31
 
      <varlistentry>
32
 
        <term>y</term>
33
 
        <listitem>
34
 
          <para>実数または複素浮動小数点数のベクトル.
35
 
            デフォルト値は <literal>x</literal>.
36
 
          </para>
37
 
        </listitem>
38
 
      </varlistentry>
39
 
      <varlistentry>
40
 
        <term>maxlags</term>
41
 
        <listitem>
42
 
          <para>スカラーで,1より大きな整数.
43
 
            デフォルト値は <literal>n</literal>. 
44
 
            ただし,<literal>n</literal>は<literal>x</literal>,
45
 
            <literal>y</literal>ベクトルの長さの大きい方です.
46
 
          </para>
47
 
        </listitem>
48
 
      </varlistentry>
49
 
      <varlistentry>
50
 
        <term>scaling</term>
51
 
        <listitem>
52
 
          <para>文字列で,値は以下のどれか:
53
 
            <literal>"biased"</literal>, <literal>"unbiased"</literal>,
54
 
            <literal>"coeff"</literal>, <literal>"none"</literal>. 
55
 
            デフォルト値は <literal>"none"</literal>.
56
 
          </para>
57
 
        </listitem>
58
 
      </varlistentry>
59
 
      <varlistentry>
60
 
        <term>c</term>
61
 
        <listitem>
62
 
          <para>実数または浮動小数点数のベクトルで,向きは
63
 
            <literal>x</literal>と同じです.
64
 
          </para>
65
 
        </listitem>
66
 
      </varlistentry>
67
 
      <varlistentry>
68
 
        <term>lagindex</term>
69
 
        <listitem>
70
 
          <para>
71
 
            行ベクトルで, <literal>c</literal>の値に
72
 
            対応する添字(lag index)を有します.
73
 
          </para>
74
 
        </listitem>
75
 
      </varlistentry>
76
 
    </variablelist>
77
 
  </refsection>
78
 
  <refsection>
79
 
    <title>説明</title>
80
 
    <itemizedlist>
81
 
      <listitem>
82
 
        <literal>c=xcorr(x)</literal>
83
 
        
84
 
        は以下のように正規化しない離散自己共分散を計算します:
85
 
        
86
 
        <latex>{\begin{matrix}C_k = \sum_{i=1}^{n-k}
87
 
          {x_{i+k}*x^{*}_i}, k \geq 0 \\ C_k = C^{*}_{-k}, k \leq
88
 
          -1\end{matrix}.$
89
 
        </latex>
90
 
        
91
 
        そして,<literal>c</literal> を返します.
92
 
        
93
 
        自己共分散の並びは,
94
 
        
95
 
        <latex>$C_k,k=-n:n$</latex>
96
 
        となります.ただし,
97
 
        <literal>n</literal>
98
 
        は
99
 
        <literal>x</literal>の長さです.
100
 
        
101
 
        
102
 
      </listitem>
103
 
      <listitem>
104
 
        <literal>xcorr(x,y)</literal>
105
 
        
106
 
        は正規化しない離散相互共分散を以下のように計算します:
107
 
        
108
 
        <latex>{\begin{matrix}C_k = \sum_{i=1}^{n-k}
109
 
          {x_{i+k}*y^{*}_i}, k \geq 0 \\ C_k = C^{*}_{-k}, k \leq
110
 
          -1\end{matrix}}.$
111
 
        </latex>
112
 
        
113
 
        結果を<literal>c</literal>に返します.
114
 
        
115
 
        
116
 
        
117
 
        相互共分散の並びは
118
 
        <latex>$C_k,k=-n:n$</latex>となります.
119
 
        ただし,<literal>n</literal>は
120
 
        <literal>x</literal>および<literal>y</literal>
121
 
        の長さの大きい方です.
122
 
      </listitem>
123
 
    </itemizedlist>
124
 
    <para>
125
 
      <literal>maxlags</literal> 引数が指定された場合,
126
 
      <literal>xcorr</literal> は <literal>c</literal> を
127
 
      返し,共分散の並びは <latex>$C_k,k=-maxlags:maxlags$</latex> と
128
 
      なります.
129
 
      <literal>maxlags</literal> が <literal>length(x)</literal>よりも
130
 
      大きい場合, <literal>c</literal>の先頭と末尾の複数の値は
131
 
      ゼロになります.
132
 
    </para>
133
 
    <para>
134
 
      <literal>scaling</literal> 引数は,
135
 
      <literal>c</literal>に結果を出力する前に
136
 
      <latex>C(k)</latex>を正規化する方法を以下のように指定します: 
137
 
      <itemizedlist>
138
 
        <listitem>
139
 
          <term>"biased"</term>:<literal>c=</literal><latex>$C$</latex><literal>/n</literal>.
140
 
        </listitem>
141
 
        <listitem>
142
 
          <term>"unbiased"</term>:<literal>c=</literal><latex>$C$</latex><literal>./(n-(-maxlags:maxlags))</literal>.
143
 
        </listitem>
144
 
        <listitem>
145
 
          <term>"coeff"</term>:<literal>c=</literal><latex>$C$</latex><literal>/(norm(x)*norm(y))</literal>.
146
 
        </listitem>
147
 
      </itemizedlist>
148
 
    </para>
149
 
  </refsection>
150
 
  <refsection>
151
 
    <title>注意</title>
152
 
    
153
 
    The
154
 
    
155
 
    <link linkend="corr">corr</link>
156
 
    関数は<literal>x</literal>および<literal>y</literal>の
157
 
    バイアス付き("biased")共分散を計算し,
158
 
    <literal>c</literal>のみを返します.
159
 
    自己共分散の並びは,<latex>$C_k,k \geq 0$</latex>となります.
160
 
  </refsection>
161
 
  <refsection>
162
 
    <refsection>
163
 
      <title>手法</title> この関数は,
164
 
      <literal>ifft(fft(x).*conj(fft(y)))</literal>により
165
 
      <latex>$C$</latex>を計算します.
166
 
    </refsection>
167
 
    <refsection>
168
 
      <title>例</title>
169
 
      <programlisting role="example">t = linspace(0, 100, 2000);
170
 
        y = 0.8 * sin(t) + 0.8 * sin(2 * t);
171
 
        [c, ind] = xcorr(y, "biased");
172
 
        plot(ind, c)    
173
 
      </programlisting>
174
 
    </refsection>
175
 
    <refsection>
176
 
      <title>参照</title>
177
 
      <simplelist type="inline">
178
 
        <member>
179
 
          <link linkend="xcov">xcov</link>
180
 
        </member>
181
 
        <member>
182
 
          <link linkend="corr">corr</link>
183
 
        </member>
184
 
        <member>
185
 
          <link linkend="fft">fft</link>
186
 
        </member>
187
 
      </simplelist>
188
 
    </refsection>
189
 
    <refsection>
190
 
      <title>作者</title>
191
 
      <simplelist type="vert">
192
 
        <member>Serge Steer, INRIA</member>
193
 
      </simplelist>
194
 
    </refsection>
195
 
    <title>使用される関数</title>
196
 
    <para>
197
 
      <link linkend="fft">fft</link>
198
 
    </para>
199
 
  </refsection>
200
 
  <refsection>
201
 
    <title>履歴</title>
202
 
    <revhistory>
203
 
      <revision>
204
 
        <revnumber>5.4.0</revnumber>
205
 
        <revremark>xcorr追加.</revremark>
206
 
      </revision>
207
 
    </revhistory>
208
 
  </refsection>
 
12
    <refnamediv>
 
13
        <refname>xcorr</refname>
 
14
        <refpurpose>離散自己/相互相関を計算する</refpurpose>
 
15
    </refnamediv>
 
16
    <refsynopsisdiv>
 
17
        <title>呼び出し手順</title>
 
18
        <synopsis>[c [,lagindex]] = xcorr(x [,maxlags [,scaling]])
 
19
            [c [,lagindex]] = xcorr(x,y [,maxlags [,scaling]])
 
20
        </synopsis>
 
21
    </refsynopsisdiv>
 
22
    <refsection>
 
23
        <title>パラメータ</title>
 
24
        <variablelist>
 
25
            <varlistentry>
 
26
                <term>x</term>
 
27
                <listitem>
 
28
                    <para>実数または複素浮動小数点数のベクトル.</para>
 
29
                </listitem>
 
30
            </varlistentry>
 
31
            <varlistentry>
 
32
                <term>y</term>
 
33
                <listitem>
 
34
                    <para>実数または複素浮動小数点数のベクトル.
 
35
                        デフォルト値は <literal>x</literal>.
 
36
                    </para>
 
37
                </listitem>
 
38
            </varlistentry>
 
39
            <varlistentry>
 
40
                <term>maxlags</term>
 
41
                <listitem>
 
42
                    <para>スカラーで,1より大きな整数.
 
43
                        デフォルト値は <literal>n</literal>. 
 
44
                        ただし,<literal>n</literal>は<literal>x</literal>,
 
45
                        <literal>y</literal>ベクトルの長さの大きい方です.
 
46
                    </para>
 
47
                </listitem>
 
48
            </varlistentry>
 
49
            <varlistentry>
 
50
                <term>scaling</term>
 
51
                <listitem>
 
52
                    <para>文字列で,値は以下のどれか:
 
53
                        <literal>"biased"</literal>, <literal>"unbiased"</literal>,
 
54
                        <literal>"coeff"</literal>, <literal>"none"</literal>. 
 
55
                        デフォルト値は <literal>"none"</literal>.
 
56
                    </para>
 
57
                </listitem>
 
58
            </varlistentry>
 
59
            <varlistentry>
 
60
                <term>c</term>
 
61
                <listitem>
 
62
                    <para>実数または浮動小数点数のベクトルで,向きは
 
63
                        <literal>x</literal>と同じです.
 
64
                    </para>
 
65
                </listitem>
 
66
            </varlistentry>
 
67
            <varlistentry>
 
68
                <term>lagindex</term>
 
69
                <listitem>
 
70
                    <para>
 
71
                        行ベクトルで, <literal>c</literal>の値に
 
72
                        対応する添字(lag index)を有します.
 
73
                    </para>
 
74
                </listitem>
 
75
            </varlistentry>
 
76
        </variablelist>
 
77
    </refsection>
 
78
    <refsection>
 
79
        <title>説明</title>
 
80
        <itemizedlist>
 
81
            <listitem>
 
82
                <literal>c=xcorr(x)</literal>
 
83
                
 
84
                は以下のように正規化しない離散自己共分散を計算します:
 
85
                
 
86
                <latex>{\begin{matrix}C_k = \sum_{i=1}^{n-k}
 
87
                    {x_{i+k}*x^{*}_i}, k \geq 0 \\ C_k = C^{*}_{-k}, k \leq
 
88
                    -1\end{matrix}.$
 
89
                </latex>
 
90
                
 
91
                そして,<literal>c</literal> を返します.
 
92
                
 
93
                自己共分散の並びは,
 
94
                
 
95
                <latex>$C_k,k=-n:n$</latex>
 
96
                となります.ただし,
 
97
                <literal>n</literal>
 
98
                は
 
99
                <literal>x</literal>の長さです.
 
100
                
 
101
                
 
102
            </listitem>
 
103
            <listitem>
 
104
                <literal>xcorr(x,y)</literal>
 
105
                
 
106
                は正規化しない離散相互共分散を以下のように計算します:
 
107
                
 
108
                <latex>{\begin{matrix}C_k = \sum_{i=1}^{n-k}
 
109
                    {x_{i+k}*y^{*}_i}, k \geq 0 \\ C_k = C^{*}_{-k}, k \leq
 
110
                    -1\end{matrix}}.$
 
111
                </latex>
 
112
                
 
113
                結果を<literal>c</literal>に返します.
 
114
                
 
115
                
 
116
                
 
117
                相互共分散の並びは
 
118
                <latex>$C_k,k=-n:n$</latex>となります.
 
119
                ただし,<literal>n</literal>は
 
120
                <literal>x</literal>および<literal>y</literal>
 
121
                の長さの大きい方です.
 
122
            </listitem>
 
123
        </itemizedlist>
 
124
        <para>
 
125
            <literal>maxlags</literal> 引数が指定された場合,
 
126
            <literal>xcorr</literal> は <literal>c</literal> を
 
127
            返し,共分散の並びは <latex>$C_k,k=-maxlags:maxlags$</latex> と
 
128
            なります.
 
129
            <literal>maxlags</literal> が <literal>length(x)</literal>よりも
 
130
            大きい場合, <literal>c</literal>の先頭と末尾の複数の値は
 
131
            ゼロになります.
 
132
        </para>
 
133
        <para>
 
134
            <literal>scaling</literal> 引数は,
 
135
            <literal>c</literal>に結果を出力する前に
 
136
            <latex>C(k)</latex>を正規化する方法を以下のように指定します: 
 
137
            <itemizedlist>
 
138
                <listitem>
 
139
                    <term>"biased"</term>:<literal>c=</literal><latex>$C$</latex><literal>/n</literal>.
 
140
                </listitem>
 
141
                <listitem>
 
142
                    <term>"unbiased"</term>:<literal>c=</literal><latex>$C$</latex><literal>./(n-(-maxlags:maxlags))</literal>.
 
143
                </listitem>
 
144
                <listitem>
 
145
                    <term>"coeff"</term>:<literal>c=</literal><latex>$C$</latex><literal>/(norm(x)*norm(y))</literal>.
 
146
                </listitem>
 
147
            </itemizedlist>
 
148
        </para>
 
149
    </refsection>
 
150
    <refsection>
 
151
        <title>注意</title>
 
152
        
 
153
        The
 
154
        
 
155
        <link linkend="corr">corr</link>
 
156
        関数は<literal>x</literal>および<literal>y</literal>の
 
157
        バイアス付き("biased")共分散を計算し,
 
158
        <literal>c</literal>のみを返します.
 
159
        自己共分散の並びは,<latex>$C_k,k \geq 0$</latex>となります.
 
160
    </refsection>
 
161
    <refsection>
 
162
        <refsection>
 
163
            <title>手法</title> この関数は,
 
164
            <literal>ifft(fft(x).*conj(fft(y)))</literal>により
 
165
            <latex>$C$</latex>を計算します.
 
166
        </refsection>
 
167
        <refsection>
 
168
            <title>例</title>
 
169
            <programlisting role="example">t = linspace(0, 100, 2000);
 
170
                y = 0.8 * sin(t) + 0.8 * sin(2 * t);
 
171
                [c, ind] = xcorr(y, "biased");
 
172
                plot(ind, c)    
 
173
            </programlisting>
 
174
        </refsection>
 
175
        <refsection>
 
176
            <title>参照</title>
 
177
            <simplelist type="inline">
 
178
                <member>
 
179
                    <link linkend="xcov">xcov</link>
 
180
                </member>
 
181
                <member>
 
182
                    <link linkend="corr">corr</link>
 
183
                </member>
 
184
                <member>
 
185
                    <link linkend="fft">fft</link>
 
186
                </member>
 
187
            </simplelist>
 
188
        </refsection>
 
189
        <refsection>
 
190
            <title>作者</title>
 
191
            <simplelist type="vert">
 
192
                <member>Serge Steer, INRIA</member>
 
193
            </simplelist>
 
194
        </refsection>
 
195
        <title>使用される関数</title>
 
196
        <para>
 
197
            <link linkend="fft">fft</link>
 
198
        </para>
 
199
    </refsection>
 
200
    <refsection>
 
201
        <title>履歴</title>
 
202
        <revhistory>
 
203
            <revision>
 
204
                <revnumber>5.4.0</revnumber>
 
205
                <revremark>xcorr追加.</revremark>
 
206
            </revision>
 
207
        </revhistory>
 
208
    </refsection>
209
209
</refentry>