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Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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cannam@95 3 <title>Real-to-Real Transform Kinds - FFTW 3.3.3</title>
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cannam@95 48 <a name="Real-to-Real-Transform-Kinds"></a>
cannam@95 49 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
cannam@95 50 <p>
cannam@95 51 Previous:&nbsp;<a rel="previous" accesskey="p" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms">Real-to-Real Transforms</a>,
cannam@95 52 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
cannam@95 53 <hr>
cannam@95 54 </div>
cannam@95 55
cannam@95 56 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
cannam@95 57
cannam@95 58 <p><a name="index-kind-_0028r2r_0029-212"></a>
cannam@95 59 FFTW currently supports 11 different r2r transform kinds, specified by
cannam@95 60 one of the constants below. For the precise definitions of these
cannam@95 61 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
cannam@95 62 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>.
cannam@95 63
cannam@95 64 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
cannam@95 65 dimension <code>N</code> that determines the normalization (and the optimal
cannam@95 66 factorization); the formula for <code>N</code> is given for each kind below.
cannam@95 67 Also, with each transform kind is listed its corrsponding inverse
cannam@95 68 transform. FFTW computes unnormalized transforms: a transform followed
cannam@95 69 by its inverse will result in the original data multiplied by <code>N</code>
cannam@95 70 (or the product of the <code>N</code>'s for each dimension, in
cannam@95 71 multi-dimensions).
cannam@95 72 <a name="index-normalization-213"></a>
cannam@95 73 <ul>
cannam@95 74 <li><a name="index-FFTW_005fR2HC-214"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in
cannam@95 75 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
cannam@95 76 size <code>n</code> stored as:
cannam@95 77 <p align=center>
cannam@95 78 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>
cannam@95 79 </p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
cannam@95 80
cannam@95 81 <li><a name="index-FFTW_005fHC2R-215"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
cannam@95 82 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
cannam@95 83
cannam@95 84 <li><a name="index-FFTW_005fDHT-216"></a><code>FFTW_DHT</code> computes a discrete Hartley transform.
cannam@95 85 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
cannam@95 86 <a name="index-discrete-Hartley-transform-217"></a>
cannam@95 87 <li><a name="index-FFTW_005fREDFT00-218"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
cannam@95 88 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
cannam@95 89 <a name="index-discrete-cosine-transform-219"></a><a name="index-DCT-220"></a>
cannam@95 90 <li><a name="index-FFTW_005fREDFT10-221"></a><code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called &ldquo;the&rdquo; DCT).
cannam@95 91 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
cannam@95 92
cannam@95 93 <li><a name="index-FFTW_005fREDFT01-222"></a><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).
cannam@95 94 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
cannam@95 95 <a name="index-IDCT-223"></a>
cannam@95 96 <li><a name="index-FFTW_005fREDFT11-224"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
cannam@95 97 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
cannam@95 98
cannam@95 99 <li><a name="index-FFTW_005fRODFT00-225"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
cannam@95 100 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
cannam@95 101 <a name="index-discrete-sine-transform-226"></a><a name="index-DST-227"></a>
cannam@95 102 <li><a name="index-FFTW_005fRODFT10-228"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
cannam@95 103 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
cannam@95 104
cannam@95 105 <li><a name="index-FFTW_005fRODFT01-229"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
cannam@95 106 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
cannam@95 107
cannam@95 108 <li><a name="index-FFTW_005fRODFT11-230"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
cannam@95 109 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
cannam@95 110
cannam@95 111 </ul>
cannam@95 112
cannam@95 113 <!-- -->
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cannam@95 115