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| author | Chris Cannam |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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| 9:c0fb53affa76 | 10:37bf6b4a2645 |
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| 1 <html lang="en"> | |
| 2 <head> | |
| 3 <title>What FFTW Really Computes - FFTW 3.3.3</title> | |
| 4 <meta http-equiv="Content-Type" content="text/html"> | |
| 5 <meta name="description" content="FFTW 3.3.3"> | |
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| 7 <link title="Top" rel="start" href="index.html#Top"> | |
| 8 <link rel="up" href="FFTW-Reference.html#FFTW-Reference" title="FFTW Reference"> | |
| 9 <link rel="prev" href="Wisdom.html#Wisdom" title="Wisdom"> | |
| 10 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> | |
| 11 <!-- | |
| 12 This manual is for FFTW | |
| 13 (version 3.3.3, 25 November 2012). | |
| 14 | |
| 15 Copyright (C) 2003 Matteo Frigo. | |
| 16 | |
| 17 Copyright (C) 2003 Massachusetts Institute of Technology. | |
| 18 | |
| 19 Permission is granted to make and distribute verbatim copies of | |
| 20 this manual provided the copyright notice and this permission | |
| 21 notice are preserved on all copies. | |
| 22 | |
| 23 Permission is granted to copy and distribute modified versions of | |
| 24 this manual under the conditions for verbatim copying, provided | |
| 25 that the entire resulting derived work is distributed under the | |
| 26 terms of a permission notice identical to this one. | |
| 27 | |
| 28 Permission is granted to copy and distribute translations of this | |
| 29 manual into another language, under the above conditions for | |
| 30 modified versions, except that this permission notice may be | |
| 31 stated in a translation approved by the Free Software Foundation. | |
| 32 --> | |
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| 44 --></style> | |
| 45 </head> | |
| 46 <body> | |
| 47 <div class="node"> | |
| 48 <a name="What-FFTW-Really-Computes"></a> | |
| 49 <p> | |
| 50 Previous: <a rel="previous" accesskey="p" href="Wisdom.html#Wisdom">Wisdom</a>, | |
| 51 Up: <a rel="up" accesskey="u" href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a> | |
| 52 <hr> | |
| 53 </div> | |
| 54 | |
| 55 <h3 class="section">4.8 What FFTW Really Computes</h3> | |
| 56 | |
| 57 <p>In this section, we provide precise mathematical definitions for the | |
| 58 transforms that FFTW computes. These transform definitions are fairly | |
| 59 standard, but some authors follow slightly different conventions for the | |
| 60 normalization of the transform (the constant factor in front) and the | |
| 61 sign of the complex exponent. We begin by presenting the | |
| 62 one-dimensional (1d) transform definitions, and then give the | |
| 63 straightforward extension to multi-dimensional transforms. | |
| 64 | |
| 65 <ul class="menu"> | |
| 66 <li><a accesskey="1" href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029">The 1d Discrete Fourier Transform (DFT)</a> | |
| 67 <li><a accesskey="2" href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT">The 1d Real-data DFT</a> | |
| 68 <li><a accesskey="3" href="1d-Real_002deven-DFTs-_0028DCTs_0029.html#g_t1d-Real_002deven-DFTs-_0028DCTs_0029">1d Real-even DFTs (DCTs)</a> | |
| 69 <li><a accesskey="4" href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029">1d Real-odd DFTs (DSTs)</a> | |
| 70 <li><a accesskey="5" href="1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html#g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029">1d Discrete Hartley Transforms (DHTs)</a> | |
| 71 <li><a accesskey="6" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a> | |
| 72 </ul> | |
| 73 | |
| 74 <!-- =========> --> | |
| 75 </body></html> | |
| 76 |