Mercurial > hg > batch-feature-extraction-tool

diff Lib/fftw-3.2.1/doc/html/.svn/text-base/The-1d-Real_002ddata-DFT.html.svn-base @ 15:585caf503ef5 tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Tidy up for ROLI
author Geogaddi\David <d.m.ronan@qmul.ac.uk>
date Tue, 17 May 2016 18:50:19 +0100
parents 636c989477e7
children
line wrap: on
line diff
--- a/Lib/fftw-3.2.1/doc/html/.svn/text-base/The-1d-Real_002ddata-DFT.html.svn-base	Wed May 04 11:02:59 2016 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,93 +0,0 @@
-<html lang="en">
-<head>
-<title>The 1d Real-data DFT - FFTW 3.2.1</title>
-<meta http-equiv="Content-Type" content="text/html">
-<meta name="description" content="FFTW 3.2.1">
-<meta name="generator" content="makeinfo 4.8">
-<link title="Top" rel="start" href="index.html#Top">
-<link rel="up" href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" title="What FFTW Really Computes">
-<link rel="prev" href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029" title="The 1d Discrete Fourier Transform (DFT)">
-<link rel="next" href="1d-Real_002deven-DFTs-_0028DCTs_0029.html#g_t1d-Real_002deven-DFTs-_0028DCTs_0029" title="1d Real-even DFTs (DCTs)">
-<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
-<!--
-This manual is for FFTW
-(version 3.2.1, 5 February 2009).
-
-Copyright (C) 2003 Matteo Frigo.
-
-Copyright (C) 2003 Massachusetts Institute of Technology.
-
-     Permission is granted to make and distribute verbatim copies of
-     this manual provided the copyright notice and this permission
-     notice are preserved on all copies.
-
-     Permission is granted to copy and distribute modified versions of
-     this manual under the conditions for verbatim copying, provided
-     that the entire resulting derived work is distributed under the
-     terms of a permission notice identical to this one.
-
-     Permission is granted to copy and distribute translations of this
-     manual into another language, under the above conditions for
-     modified versions, except that this permission notice may be
-     stated in a translation approved by the Free Software Foundation.
-   -->
-<meta http-equiv="Content-Style-Type" content="text/css">
-<style type="text/css"><!--
-  pre.display { font-family:inherit }
-  pre.format  { font-family:inherit }
-  pre.smalldisplay { font-family:inherit; font-size:smaller }
-  pre.smallformat  { font-family:inherit; font-size:smaller }
-  pre.smallexample { font-size:smaller }
-  pre.smalllisp    { font-size:smaller }
-  span.sc    { font-variant:small-caps }
-  span.roman { font-family:serif; font-weight:normal; } 
-  span.sansserif { font-family:sans-serif; font-weight:normal; } 
---></style>
-</head>
-<body>
-<div class="node">
-<p>
-<a name="The-1d-Real-data-DFT"></a>
-<a name="The-1d-Real_002ddata-DFT"></a>
-Next:&nbsp;<a rel="next" accesskey="n" href="1d-Real_002deven-DFTs-_0028DCTs_0029.html#g_t1d-Real_002deven-DFTs-_0028DCTs_0029">1d Real-even DFTs (DCTs)</a>,
-Previous:&nbsp;<a rel="previous" accesskey="p" href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029">The 1d Discrete Fourier Transform (DFT)</a>,
-Up:&nbsp;<a rel="up" accesskey="u" href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>
-<hr>
-</div>
-
-<h4 class="subsection">4.8.2 The 1d Real-data DFT</h4>
-
-<p>The real-input (r2c) DFT in FFTW computes the <em>forward</em> transform
-Y of the size <code>n</code> real array X, exactly as defined
-above, i.e. 
-<center><img src="equation-dft.png" align="top">.</center>This output array Y can easily be shown to possess the
-&ldquo;Hermitian&rdquo; symmetry
-<a name="index-Hermitian-286"></a><i>Y<sub>k</sub> = Y<sub>n-k</sub></i><sup>*</sup>,where we take Y to be periodic so that
-<i>Y<sub>n</sub> = Y</i><sub>0</sub>.
-
-   <p>As a result of this symmetry, half of the output Y is redundant
-(being the complex conjugate of the other half), and so the 1d r2c
-transforms only output elements 0<small class="dots">...</small>n/2 of Y
-(n/2+1 complex numbers), where the division by 2 is
-rounded down.
-
-   <p>Moreover, the Hermitian symmetry implies that
-<i>Y</i><sub>0</sub>and, if n is even, the
-<i>Y</i><sub><i>n</i>/2</sub>element, are purely real.  So, for the <code>R2HC</code> r2r transform, these
-elements are not stored in the halfcomplex output format. 
-<a name="index-r2r-287"></a><a name="index-R2HC-288"></a><a name="index-halfcomplex-format-289"></a>
-The c2r and <code>H2RC</code> r2r transforms compute the backward DFT of the
-<em>complex</em> array X with Hermitian symmetry, stored in the
-r2c/<code>R2HC</code> output formats, respectively, where the backward
-transform is defined exactly as for the complex case:
-<center><img src="equation-idft.png" align="top">.</center>The outputs <code>Y</code> of this transform can easily be seen to be purely
-real, and are stored as an array of real numbers.
-
-   <p><a name="index-normalization-290"></a>Like FFTW's complex DFT, these transforms are unnormalized.  In other
-words, applying the real-to-complex (forward) and then the
-complex-to-real (backward) transform will multiply the input by
-n.
-
-<!-- =========> -->
-</body></html>
-