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Viewing changes to man/fr/signal/corr.xml

  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

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man/fr/signal/corr.xml
 
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<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
 
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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
 
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<MAN>
 
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  <LANGUAGE>eng</LANGUAGE>
 
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  <TITLE>corr</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>April 1993</DATE>
 
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  <SHORT_DESCRIPTION name="corr"> correlation, covariance</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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    <CALLING_SEQUENCE_ITEM>[cov,Mean]=corr(x,[y],nlags)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[cov,Mean]=corr('fft',xmacro,[ymacro],n,sect)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[w,xu]=corr('updt',x1,[y1],w0)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[w,xu]=corr('updt',x2,[y2],w,xu)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM> ...  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[wk]=corr('updt',xk,[yk],w,xu)  </CALLING_SEQUENCE_ITEM>
 
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  </CALLING_SEQUENCE>
 
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  <PARAM>
 
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    <PARAM_INDENT>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>x</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a real vector</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>y</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a real vector, default value x.</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>nlags</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: integer, number of correlation coefficients desired.</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>xmacro</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a scilab external (see below).</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>ymacro</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a scilab external (see below), default value xmacro</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>n</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: an integer, total size of the sequence (see below).</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>sect</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: size of sections of the sequence (see below).</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>xi</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a real vector</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>yi</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a real vector,default value xi.</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>cov</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real vector, the correlation coefficients</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>Mean</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real number or vector,  the mean of x and if given y</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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    </PARAM_INDENT>
 
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  </PARAM>
 
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  <DESCRIPTION>
 
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    <P>
 
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    Computes
 
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  </P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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                n - m 
 
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                 ====
 
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                 \                                                 1
 
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        cov(m) =  >        (x(k)  - xmean) (y(m+k)      - ymean) * ---
 
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                 /                                                  n
 
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                 ====
 
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                 k = 1
 
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   ]]>
 
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    </VERBATIM>
 
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    <P>
 
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    for   m=0,..,<VERB>nlag-1</VERB> and two vectors <VERB>x=[x(1),..,x(n)]</VERB>
 
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     <VERB>y=[y(1),..,y(n)]</VERB>
 
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  </P>
 
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    <P>
 
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    Note that if x and y sequences are differents corr(x,y,...) is
 
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    different with corr(y,x,...)
 
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  </P>
 
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    <DESCRIPTION_INDENT>
 
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      <DESCRIPTION_ITEM label="Short sequences">
 
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        <SP><VERB>[cov,Mean]=corr(x,[y],nlags)</VERB> returns the first nlags
 
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    correlation coefficients and Mean = <VERB>mean(x)</VERB>
 
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    (mean of <VERB>[x,y]</VERB> if <VERB>y</VERB> is an argument).
 
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    The sequence <VERB>x</VERB> (resp. <VERB>y</VERB>) is assumed real, and <VERB>x</VERB> 
 
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    and <VERB>y</VERB> are of same dimension n.</SP>
 
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      </DESCRIPTION_ITEM>
 
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      <DESCRIPTION_ITEM label="Long sequences">
 
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        <SP><VERB>[cov,Mean]=corr('fft',xmacro,[ymacro],n,sect)</VERB> Here <VERB>xmacro</VERB> is either</SP>
 
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        <DESCRIPTION_INDENT>
 
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          <DESCRIPTION_ITEM>
 
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            <P> 
 
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        a function of type <VERB>[xx]=xmacro(sect,istart)</VERB> which
 
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        returns a vector <VERB>xx</VERB> of dimension
 
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        <VERB>nsect</VERB> containing the part of the sequence with
 
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        indices from <VERB>istart</VERB> to
 
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        <VERB>istart+sect-1</VERB>.</P>
 
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          </DESCRIPTION_ITEM>
 
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          <DESCRIPTION_ITEM>
 
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            <P>
 
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        a fortran subroutine or C procedure which performs the same
 
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        calculation. (See the source code of <VERB>dgetx</VERB> for an
 
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        example). <VERB>n</VERB> = total size of the
 
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        sequence. <VERB>sect</VERB> = size of sections of the
 
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        sequence. <VERB>sect</VERB> must be a power of
 
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        2. <VERB>cov</VERB> has dimension
 
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        <VERB>sect</VERB>. Calculation is performed by FFT.</P>
 
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          </DESCRIPTION_ITEM>
 
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        </DESCRIPTION_INDENT>
 
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      </DESCRIPTION_ITEM>
 
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      <DESCRIPTION_ITEM label="Updating method">
 
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        <VERBATIM>
 
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<![CDATA[
 
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    [w,xu]=corr('updt',x1,[y1],w0)
 
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    [w,xu]=corr('updt',x2,[y2],w,xu)
 
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     ...
 
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    wk=corr('updt',xk,[yk],w,xu)
 
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    ]]>
 
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        </VERBATIM>
 
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        <P>
 
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    With this calling sequence the calculation is updated at each
 
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    call to <VERB>corr</VERB>.</P>
 
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        <VERBATIM>
 
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<![CDATA[
 
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    w0 = 0*ones(1,2*nlags);
 
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    nlags = power of 2.
 
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    ]]>
 
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        </VERBATIM>
 
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        <P><VERB>x1,x2,...</VERB> are parts of <VERB>x</VERB> such that
 
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    <VERB>x=[x1,x2,...]</VERB> and sizes of <VERB>xi</VERB> a power of
 
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    2.  To get <VERB>nlags</VERB> coefficients a final fft must be
 
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    performed <VERB>c=fft(w,1)/n</VERB>; <VERB>cov=c(1nlags)</VERB>
 
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    (<VERB>n</VERB> is the size of <VERB>x (y)</VERB>).  Caution: this
 
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    calling sequence assumes that <VERB>xmean = ymean = 0</VERB>.</P>
 
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      </DESCRIPTION_ITEM>
 
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    </DESCRIPTION_INDENT>
 
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  </DESCRIPTION>
 
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  <EXAMPLE>
 
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<![CDATA[
 
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x=%pi/10:%pi/10:102.4*%pi;
 
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rand('seed');rand('normal');
 
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y=[.8*sin(x)+.8*sin(2*x)+rand(x);.8*sin(x)+.8*sin(1.99*x)+rand(x)];
 
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c=[];
 
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for j=1:2,for k=1:2,c=[c;corr(y(k,:),y(j,:),64)];end;end;
 
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c=matrix(c,2,128);cov=[];
 
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for j=1:64,cov=[cov;c(:,(j-1)*2+1:2*j)];end;
 
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rand('unif')
 
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//
 
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rand('normal');x=rand(1,256);y=-x;
 
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deff('[z]=xx(inc,is)','z=x(is:is+inc-1)');
 
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deff('[z]=yy(inc,is)','z=y(is:is+inc-1)');
 
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[c,mxy]=corr(x,y,32);
 
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x=x-mxy(1)*ones(x);y=y-mxy(2)*ones(y);  //centring
 
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c1=corr(x,y,32);c2=corr(x,32);
 
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norm(c1+c2,1)
 
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[c3,m3]=corr('fft',xx,yy,256,32);
 
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norm(c1-c3,1)
 
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[c4,m4]=corr('fft',xx,256,32);
 
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norm(m3,1),norm(m4,1)
 
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norm(c3-c1,1),norm(c4-c2,1)
 
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x1=x(1:128);x2=x(129:256);
 
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y1=y(1:128);y2=y(129:256);
 
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w0=0*ones(1:64);   //32 coeffs
 
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[w1,xu]=corr('u',x1,y1,w0);w2=corr('u',x2,y2,w1,xu);
 
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zz=real(fft(w2,1))/256;c5=zz(1:32);
 
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norm(c5-c1,1)
 
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[w1,xu]=corr('u',x1,w0);w2=corr('u',x2,w1,xu);
 
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zz=real(fft(w2,1))/256;c6=zz(1:32);
 
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norm(c6-c2,1)
 
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rand('unif')
 
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// test for Fortran or C external 
 
203
//
 
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deff('[y]=xmacro(sec,ist)','y=sin(ist:(ist+sec-1))');
 
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x=xmacro(100,1);
 
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[cc1,mm1]=corr(x,2^3);
 
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[cc,mm]=corr('fft',xmacro,100,2^3);
 
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[cc2,mm2]=corr('fft','corexx',100,2^3);
 
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[maxi(abs(cc-cc1)),maxi(abs(mm-mm1)),maxi(abs(cc-cc2)),maxi(abs(mm-mm2))]
 
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deff('[y]=ymacro(sec,ist)','y=cos(ist:(ist+sec-1))');
 
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y=ymacro(100,1);
 
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[cc1,mm1]=corr(x,y,2^3);
 
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[cc,mm]=corr('fft',xmacro,ymacro,100,2^3);
 
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[cc2,mm2]=corr('fft','corexx','corexy',100,2^3);
 
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[maxi(abs(cc-cc1)),maxi(abs(mm-mm1)),maxi(abs(cc-cc2)),maxi(abs(mm-mm2))]
 
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218
 ]]>
 
219
  </EXAMPLE>
 
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  <SEE_ALSO>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>fft</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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</MAN>