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diff src/fftw-3.3.3/doc/html/Real_002dto_002dReal-Transform-Kinds.html @ 10:37bf6b4a2645
Add FFTW3
| author | Chris Cannam |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.3/doc/html/Real_002dto_002dReal-Transform-Kinds.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,115 @@ +<html lang="en"> +<head> +<title>Real-to-Real Transform Kinds - FFTW 3.3.3</title> +<meta http-equiv="Content-Type" content="text/html"> +<meta name="description" content="FFTW 3.3.3"> +<meta name="generator" content="makeinfo 4.13"> +<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 3.3.3, 25 November 2012). + +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"> +<a name="Real-to-Real-Transform-Kinds"></a> +<a name="Real_002dto_002dReal-Transform-Kinds"></a> +<p> +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_0029-212"></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-213"></a> + <ul> +<li><a name="index-FFTW_005fR2HC-214"></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-215"></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-216"></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-217"></a> +<li><a name="index-FFTW_005fREDFT00-218"></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-219"></a><a name="index-DCT-220"></a> +<li><a name="index-FFTW_005fREDFT10-221"></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_005fREDFT01-222"></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-223"></a> +<li><a name="index-FFTW_005fREDFT11-224"></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_005fRODFT00-225"></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-226"></a><a name="index-DST-227"></a> +<li><a name="index-FFTW_005fRODFT10-228"></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_005fRODFT01-229"></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_005fRODFT11-230"></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> +