1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from xcorr1.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="xcorr1" xml:lang="en"
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:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>xcorr1</refname>
<refpurpose>Estimates the cross-correlation.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[R, lag] = xcorr1 (X, Y, maxlag, scale)
[R, lag] = xcorr1 (X, Y, maxlag)
[R, lag] = xcorr1 (X, Y)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>X:</term>
<listitem><para> [non-empty; real or complex; vector or matrix] data.</para></listitem></varlistentry>
<varlistentry><term>Y:</term>
<listitem><para> [real or complex vector] data.</para></listitem></varlistentry>
<varlistentry><term>maxlag:</term>
<listitem><para> [integer scalar] maximum correlation lag If omitted, the default value is N-1, where N is the greater of the lengths of X and Y or, if X is a matrix, the number of rows in X.</para></listitem></varlistentry>
<varlistentry><term>scale:</term>
<listitem><para> [character string] specifies the type of scaling applied to the correlation vector (or matrix). is one of:</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
This is an Octave function.
Estimate the cross correlation R_xy(k) of vector arguments X and Y or, if Y is omitted, estimate autocorrelation R_xx(k) of vector X, for a range of lags k specified by argument "maxlag". If X is a
matrix, each column of X is correlated with itself and every other column.
</para>
<para>
The cross-correlation estimate between vectors "x" and "y" (of length N) for lag "k" is given by
</para>
<para>
N
R_xy(k) = sum x_{i+k} conj(y_i),
i=1
</para>
<para>
where data not provided (for example x(-1), y(N+1)) is zero. Note the definition of cross-correlation given above. To compute a cross-correlation consistent with the field of statistics, see xcov.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
[R, lag] = xcorr1 ( [5 5], [2 2], 2, 'biased' )
R =
0 5 10 5 0
lag =
-2 -1 0 1 2
]]></programlisting>
</refsection>
</refentry>
|
