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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents d0c2a83c1364
children
rev   line source
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Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
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Chris@82 6 Copyright (C) 2003 Matteo Frigo.
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Real-to-Real Transform Kinds</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: Real-to-Real Transform Kinds">
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Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Previous: <a href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" accesskey="p" rel="prev">Real-to-Real Transforms</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Real_002dto_002dReal-Transform-Kinds-1"></a>
Chris@82 78 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
Chris@82 79 <a name="index-kind-_0028r2r_0029-1"></a>
Chris@82 80
Chris@82 81 <p>FFTW currently supports 11 different r2r transform kinds, specified by
Chris@82 82 one of the constants below. For the precise definitions of these
Chris@82 83 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
Chris@82 84 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>.
Chris@82 85 </p>
Chris@82 86 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
Chris@82 87 dimension <code>N</code> that determines the normalization (and the optimal
Chris@82 88 factorization); the formula for <code>N</code> is given for each kind below.
Chris@82 89 Also, with each transform kind is listed its corrsponding inverse
Chris@82 90 transform. FFTW computes unnormalized transforms: a transform followed
Chris@82 91 by its inverse will result in the original data multiplied by <code>N</code>
Chris@82 92 (or the product of the <code>N</code>&rsquo;s for each dimension, in
Chris@82 93 multi-dimensions).
Chris@82 94 <a name="index-normalization-7"></a>
Chris@82 95 </p>
Chris@82 96 <ul>
Chris@82 97 <li> <a name="index-FFTW_005fR2HC-1"></a>
Chris@82 98 <code>FFTW_R2HC</code> computes a real-input DFT with output in
Chris@82 99 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
Chris@82 100 size <code>n</code> stored as:
Chris@82 101 <p align=center>
Chris@82 102 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>
Chris@82 103 </p>
Chris@82 104 (Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
Chris@82 105
Chris@82 106 </li><li> <a name="index-FFTW_005fHC2R-1"></a>
Chris@82 107 <code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
Chris@82 108 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
Chris@82 109
Chris@82 110 </li><li> <a name="index-FFTW_005fDHT-1"></a>
Chris@82 111 <code>FFTW_DHT</code> computes a discrete Hartley transform.
Chris@82 112 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
Chris@82 113 <a name="index-discrete-Hartley-transform-1"></a>
Chris@82 114
Chris@82 115 </li><li> <a name="index-FFTW_005fREDFT00-2"></a>
Chris@82 116 <code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
Chris@82 117 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
Chris@82 118 <a name="index-discrete-cosine-transform-1"></a>
Chris@82 119 <a name="index-DCT-1"></a>
Chris@82 120
Chris@82 121 </li><li> <a name="index-FFTW_005fREDFT10-1"></a>
Chris@82 122 <code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called &ldquo;the&rdquo; DCT).
Chris@82 123 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
Chris@82 124
Chris@82 125 </li><li> <a name="index-FFTW_005fREDFT01-1"></a>
Chris@82 126 <code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called &ldquo;the&rdquo; IDCT, being the inverse of DCT-II).
Chris@82 127 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
Chris@82 128 <a name="index-IDCT-2"></a>
Chris@82 129
Chris@82 130 </li><li> <a name="index-FFTW_005fREDFT11-1"></a>
Chris@82 131 <code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
Chris@82 132 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
Chris@82 133
Chris@82 134 </li><li> <a name="index-FFTW_005fRODFT00-1"></a>
Chris@82 135 <code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
Chris@82 136 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
Chris@82 137 <a name="index-discrete-sine-transform-1"></a>
Chris@82 138 <a name="index-DST-1"></a>
Chris@82 139
Chris@82 140 </li><li> <a name="index-FFTW_005fRODFT10-1"></a>
Chris@82 141 <code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
Chris@82 142 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
Chris@82 143
Chris@82 144 </li><li> <a name="index-FFTW_005fRODFT01-1"></a>
Chris@82 145 <code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
Chris@82 146 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
Chris@82 147
Chris@82 148 </li><li> <a name="index-FFTW_005fRODFT11-1"></a>
Chris@82 149 <code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
Chris@82 150 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
Chris@82 151
Chris@82 152 </li></ul>
Chris@82 153
Chris@82 154 <hr>
Chris@82 155 <div class="header">
Chris@82 156 <p>
Chris@82 157 Previous: <a href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" accesskey="p" rel="prev">Real-to-Real Transforms</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 158 </div>
Chris@82 159
Chris@82 160
Chris@82 161
Chris@82 162 </body>
Chris@82 163 </html>