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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 37bf6b4a2645
children
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Chris@10 1 <html lang="en">
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Chris@10 3 <title>Real-to-Real Transform Kinds - FFTW 3.3.3</title>
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Chris@10 47 <div class="node">
Chris@10 48 <a name="Real-to-Real-Transform-Kinds"></a>
Chris@10 49 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
Chris@10 50 <p>
Chris@10 51 Previous:&nbsp;<a rel="previous" accesskey="p" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms">Real-to-Real Transforms</a>,
Chris@10 52 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
Chris@10 53 <hr>
Chris@10 54 </div>
Chris@10 55
Chris@10 56 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
Chris@10 57
Chris@10 58 <p><a name="index-kind-_0028r2r_0029-212"></a>
Chris@10 59 FFTW currently supports 11 different r2r transform kinds, specified by
Chris@10 60 one of the constants below. For the precise definitions of these
Chris@10 61 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
Chris@10 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>.
Chris@10 63
Chris@10 64 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
Chris@10 65 dimension <code>N</code> that determines the normalization (and the optimal
Chris@10 66 factorization); the formula for <code>N</code> is given for each kind below.
Chris@10 67 Also, with each transform kind is listed its corrsponding inverse
Chris@10 68 transform. FFTW computes unnormalized transforms: a transform followed
Chris@10 69 by its inverse will result in the original data multiplied by <code>N</code>
Chris@10 70 (or the product of the <code>N</code>'s for each dimension, in
Chris@10 71 multi-dimensions).
Chris@10 72 <a name="index-normalization-213"></a>
Chris@10 73 <ul>
Chris@10 74 <li><a name="index-FFTW_005fR2HC-214"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in
Chris@10 75 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
Chris@10 76 size <code>n</code> stored as:
Chris@10 77 <p align=center>
Chris@10 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>
Chris@10 79 </p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
Chris@10 80
Chris@10 81 <li><a name="index-FFTW_005fHC2R-215"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
Chris@10 82 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
Chris@10 83
Chris@10 84 <li><a name="index-FFTW_005fDHT-216"></a><code>FFTW_DHT</code> computes a discrete Hartley transform.
Chris@10 85 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
Chris@10 86 <a name="index-discrete-Hartley-transform-217"></a>
Chris@10 87 <li><a name="index-FFTW_005fREDFT00-218"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
Chris@10 88 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
Chris@10 89 <a name="index-discrete-cosine-transform-219"></a><a name="index-DCT-220"></a>
Chris@10 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).
Chris@10 91 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
Chris@10 92
Chris@10 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).
Chris@10 94 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
Chris@10 95 <a name="index-IDCT-223"></a>
Chris@10 96 <li><a name="index-FFTW_005fREDFT11-224"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
Chris@10 97 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
Chris@10 98
Chris@10 99 <li><a name="index-FFTW_005fRODFT00-225"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
Chris@10 100 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
Chris@10 101 <a name="index-discrete-sine-transform-226"></a><a name="index-DST-227"></a>
Chris@10 102 <li><a name="index-FFTW_005fRODFT10-228"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
Chris@10 103 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
Chris@10 104
Chris@10 105 <li><a name="index-FFTW_005fRODFT01-229"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
Chris@10 106 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
Chris@10 107
Chris@10 108 <li><a name="index-FFTW_005fRODFT11-230"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
Chris@10 109 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
Chris@10 110
Chris@10 111 </ul>
Chris@10 112
Chris@10 113 <!-- -->
Chris@10 114 </body></html>
Chris@10 115