Mercurial > hg > batch-feature-extraction-tool
diff Lib/fftw-3.2.1/doc/html/.svn/text-base/Real_002dto_002dReal-Transform-Kinds.html.svn-base @ 15:585caf503ef5 tip
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 |
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--- a/Lib/fftw-3.2.1/doc/html/.svn/text-base/Real_002dto_002dReal-Transform-Kinds.html.svn-base Wed May 04 11:02:59 2016 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,115 +0,0 @@ -<html lang="en"> -<head> -<title>Real-to-Real Transform Kinds - 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="Basic-Interface.html#Basic-Interface" title="Basic Interface"> -<link rel="prev" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" title="Real-to-Real Transforms"> -<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="Real-to-Real-Transform-Kinds"></a> -<a name="Real_002dto_002dReal-Transform-Kinds"></a> -Previous: <a rel="previous" accesskey="p" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms">Real-to-Real Transforms</a>, -Up: <a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a> -<hr> -</div> - -<h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4> - -<p><a name="index-kind-_0028r2r_0029-203"></a> -FFTW currently supports 11 different r2r transform kinds, specified by -one of the constants below. For the precise definitions of these -transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial -introduction to these transform kinds, see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>. - - <p>For dimension of size <code>n</code>, there is a corresponding “logical” -dimension <code>N</code> that determines the normalization (and the optimal -factorization); the formula for <code>N</code> is given for each kind below. -Also, with each transform kind is listed its corrsponding inverse -transform. FFTW computes unnormalized transforms: a transform followed -by its inverse will result in the original data multiplied by <code>N</code> -(or the product of the <code>N</code>'s for each dimension, in -multi-dimensions). -<a name="index-normalization-204"></a> - <ul> -<li><a name="index-FFTW_005fR2HC-205"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in -“halfcomplex” format, i.e. real and imaginary parts for a transform of -size <code>n</code> stored as: -<p align=center> -r<sub>0</sub>, r<sub>1</sub>, r<sub>2</sub>, ..., r<sub>n/2</sub>, i<sub>(n+1)/2-1</sub>, ..., i<sub>2</sub>, i<sub>1</sub> -</p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.) - - <li><a name="index-FFTW_005fHC2R-206"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above. -(Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.) - - <li><a name="index-FFTW_005fDHT-207"></a><code>FFTW_DHT</code> computes a discrete Hartley transform. -(Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.) -<a name="index-discrete-Hartley-transform-208"></a> -<li><a name="index-FFTW_005fREDFT00-209"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I. -(Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.) -<a name="index-discrete-cosine-transform-210"></a><a name="index-DCT-211"></a> -<li><a name="index-FFTW_005fREDFT10-212"></a><code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT). -(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.) - - <li><a name="index-FFTW_005fREDFT01-213"></a><code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II). -(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.) -<a name="index-IDCT-214"></a> -<li><a name="index-FFTW_005fREDFT11-215"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV. -(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.) - - <li><a name="index-FFTW_005fRODFT00-216"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I. -(Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.) -<a name="index-discrete-sine-transform-217"></a><a name="index-DST-218"></a> -<li><a name="index-FFTW_005fRODFT10-219"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II. -(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.) - - <li><a name="index-FFTW_005fRODFT01-220"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III. -(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.) - - <li><a name="index-FFTW_005fRODFT11-221"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV. -(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.) - - </ul> - -<!-- --> -</body></html> -