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2 <head>
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3 <title>What FFTW Really Computes - FFTW 3.3.3</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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5 <meta name="description" content="FFTW 3.3.3">
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6 <meta name="generator" content="makeinfo 4.13">
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7 <link title="Top" rel="start" href="index.html#Top">
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8 <link rel="up" href="FFTW-Reference.html#FFTW-Reference" title="FFTW Reference">
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9 <link rel="prev" href="Wisdom.html#Wisdom" title="Wisdom">
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10 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
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11 <!--
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12 This manual is for FFTW
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13 (version 3.3.3, 25 November 2012).
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14
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15 Copyright (C) 2003 Matteo Frigo.
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16
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17 Copyright (C) 2003 Massachusetts Institute of Technology.
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18
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19 Permission is granted to make and distribute verbatim copies of
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20 this manual provided the copyright notice and this permission
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21 notice are preserved on all copies.
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22
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23 Permission is granted to copy and distribute modified versions of
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24 this manual under the conditions for verbatim copying, provided
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25 that the entire resulting derived work is distributed under the
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26 terms of a permission notice identical to this one.
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27
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28 Permission is granted to copy and distribute translations of this
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29 manual into another language, under the above conditions for
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30 modified versions, except that this permission notice may be
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31 stated in a translation approved by the Free Software Foundation.
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32 -->
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44 --></style>
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45 </head>
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46 <body>
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47 <div class="node">
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48 <a name="What-FFTW-Really-Computes"></a>
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49 <p>
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50 Previous: <a rel="previous" accesskey="p" href="Wisdom.html#Wisdom">Wisdom</a>,
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51 Up: <a rel="up" accesskey="u" href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>
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52 <hr>
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53 </div>
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54
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55 <h3 class="section">4.8 What FFTW Really Computes</h3>
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56
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57 <p>In this section, we provide precise mathematical definitions for the
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58 transforms that FFTW computes. These transform definitions are fairly
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59 standard, but some authors follow slightly different conventions for the
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60 normalization of the transform (the constant factor in front) and the
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61 sign of the complex exponent. We begin by presenting the
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62 one-dimensional (1d) transform definitions, and then give the
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63 straightforward extension to multi-dimensional transforms.
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64
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65 <ul class="menu">
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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>
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67 <li><a accesskey="2" href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT">The 1d Real-data DFT</a>
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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>
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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>
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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>
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71 <li><a accesskey="6" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a>
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72 </ul>
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73
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74 <!-- =========> -->
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75 </body></html>
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76
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