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Fixed Spectral Contrast and Periodicity
author Geogaddi\David <d.m.ronan@qmul.ac.uk>
date Mon, 17 Aug 2015 19:16:33 +0100
parents 25bf17994ef1
children
rev   line source
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d@0 3 <title>Real-to-Real Transform Kinds - FFTW 3.2.1</title>
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d@0 47 <div class="node">
d@0 48 <p>
d@0 49 <a name="Real-to-Real-Transform-Kinds"></a>
d@0 50 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
d@0 51 Previous:&nbsp;<a rel="previous" accesskey="p" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms">Real-to-Real Transforms</a>,
d@0 52 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
d@0 53 <hr>
d@0 54 </div>
d@0 55
d@0 56 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
d@0 57
d@0 58 <p><a name="index-kind-_0028r2r_0029-203"></a>
d@0 59 FFTW currently supports 11 different r2r transform kinds, specified by
d@0 60 one of the constants below. For the precise definitions of these
d@0 61 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
d@0 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>.
d@0 63
d@0 64 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
d@0 65 dimension <code>N</code> that determines the normalization (and the optimal
d@0 66 factorization); the formula for <code>N</code> is given for each kind below.
d@0 67 Also, with each transform kind is listed its corrsponding inverse
d@0 68 transform. FFTW computes unnormalized transforms: a transform followed
d@0 69 by its inverse will result in the original data multiplied by <code>N</code>
d@0 70 (or the product of the <code>N</code>'s for each dimension, in
d@0 71 multi-dimensions).
d@0 72 <a name="index-normalization-204"></a>
d@0 73 <ul>
d@0 74 <li><a name="index-FFTW_005fR2HC-205"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in
d@0 75 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
d@0 76 size <code>n</code> stored as:
d@0 77 <p align=center>
d@0 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>
d@0 79 </p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
d@0 80
d@0 81 <li><a name="index-FFTW_005fHC2R-206"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
d@0 82 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
d@0 83
d@0 84 <li><a name="index-FFTW_005fDHT-207"></a><code>FFTW_DHT</code> computes a discrete Hartley transform.
d@0 85 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
d@0 86 <a name="index-discrete-Hartley-transform-208"></a>
d@0 87 <li><a name="index-FFTW_005fREDFT00-209"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
d@0 88 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
d@0 89 <a name="index-discrete-cosine-transform-210"></a><a name="index-DCT-211"></a>
d@0 90 <li><a name="index-FFTW_005fREDFT10-212"></a><code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called &ldquo;the&rdquo; DCT).
d@0 91 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
d@0 92
d@0 93 <li><a name="index-FFTW_005fREDFT01-213"></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).
d@0 94 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
d@0 95 <a name="index-IDCT-214"></a>
d@0 96 <li><a name="index-FFTW_005fREDFT11-215"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
d@0 97 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
d@0 98
d@0 99 <li><a name="index-FFTW_005fRODFT00-216"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
d@0 100 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
d@0 101 <a name="index-discrete-sine-transform-217"></a><a name="index-DST-218"></a>
d@0 102 <li><a name="index-FFTW_005fRODFT10-219"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
d@0 103 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
d@0 104
d@0 105 <li><a name="index-FFTW_005fRODFT01-220"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
d@0 106 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
d@0 107
d@0 108 <li><a name="index-FFTW_005fRODFT11-221"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
d@0 109 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
d@0 110
d@0 111 </ul>
d@0 112
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