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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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2 <html>
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3 <!-- This manual is for FFTW
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4 (version 3.3.5, 30 July 2016).
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5
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6 Copyright (C) 2003 Matteo Frigo.
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7
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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9
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10 Permission is granted to make and distribute verbatim copies of this
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11 manual provided the copyright notice and this permission notice are
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12 preserved on all copies.
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14 Permission is granted to copy and distribute modified versions of this
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15 manual under the conditions for verbatim copying, provided that the
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16 entire resulting derived work is distributed under the terms of a
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17 permission notice identical to this one.
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18
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19 Permission is granted to copy and distribute translations of this manual
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24 <head>
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25 <title>FFTW 3.3.5: What FFTW Really Computes</title>
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26
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27 <meta name="description" content="FFTW 3.3.5: What FFTW Really Computes">
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34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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36 <link href="FFTW-Reference.html#FFTW-Reference" rel="up" title="FFTW Reference">
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37 <link href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029" rel="next" title="The 1d Discrete Fourier Transform (DFT)">
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66 </style>
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67
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69 </head>
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70
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71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
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72 <a name="What-FFTW-Really-Computes"></a>
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73 <div class="header">
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74 <p>
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75 Previous: <a href="Wisdom.html#Wisdom" accesskey="p" rel="prev">Wisdom</a>, Up: <a href="FFTW-Reference.html#FFTW-Reference" accesskey="u" rel="up">FFTW Reference</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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76 </div>
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77 <hr>
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78 <a name="What-FFTW-Really-Computes-1"></a>
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79 <h3 class="section">4.8 What FFTW Really Computes</h3>
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80
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81 <p>In this section, we provide precise mathematical definitions for the
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82 transforms that FFTW computes. These transform definitions are fairly
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83 standard, but some authors follow slightly different conventions for the
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84 normalization of the transform (the constant factor in front) and the
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85 sign of the complex exponent. We begin by presenting the
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86 one-dimensional (1d) transform definitions, and then give the
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87 straightforward extension to multi-dimensional transforms.
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88 </p>
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89 <table class="menu" border="0" cellspacing="0">
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90 <tr><td align="left" valign="top">• <a href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029" accesskey="1">The 1d Discrete Fourier Transform (DFT)</a>:</td><td> </td><td align="left" valign="top">
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91 </td></tr>
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92 <tr><td align="left" valign="top">• <a href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT" accesskey="2">The 1d Real-data DFT</a>:</td><td> </td><td align="left" valign="top">
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93 </td></tr>
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94 <tr><td align="left" valign="top">• <a href="1d-Real_002deven-DFTs-_0028DCTs_0029.html#g_t1d-Real_002deven-DFTs-_0028DCTs_0029" accesskey="3">1d Real-even DFTs (DCTs)</a>:</td><td> </td><td align="left" valign="top">
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95 </td></tr>
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96 <tr><td align="left" valign="top">• <a href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029" accesskey="4">1d Real-odd DFTs (DSTs)</a>:</td><td> </td><td align="left" valign="top">
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97 </td></tr>
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98 <tr><td align="left" valign="top">• <a href="1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html#g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029" accesskey="5">1d Discrete Hartley Transforms (DHTs)</a>:</td><td> </td><td align="left" valign="top">
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99 </td></tr>
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100 <tr><td align="left" valign="top">• <a href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" accesskey="6">Multi-dimensional Transforms</a>:</td><td> </td><td align="left" valign="top">
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101 </td></tr>
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102 </table>
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103
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104
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105
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106
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107 </body>
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108 </html>
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