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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam
date Tue, 19 Nov 2019 14:52:55 +0000
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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>