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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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3 <!-- This manual is for FFTW
4 (version 3.3.5, 30 July 2016).
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6 Copyright (C) 2003 Matteo Frigo.
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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25 <title>FFTW 3.3.5: What FFTW Really Computes</title>
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
36 <link href="FFTW-Reference.html#FFTW-Reference" rel="up" title="FFTW Reference">
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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72 <a name="What-FFTW-Really-Computes"></a>
73 <div class="header">
74 <p>
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> &nbsp; [<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>
76 </div>
77 <hr>
78 <a name="What-FFTW-Really-Computes-1"></a>
79 <h3 class="section">4.8 What FFTW Really Computes</h3>
80
81 <p>In this section, we provide precise mathematical definitions for the
82 transforms that FFTW computes. These transform definitions are fairly
83 standard, but some authors follow slightly different conventions for the
84 normalization of the transform (the constant factor in front) and the
85 sign of the complex exponent. We begin by presenting the
86 one-dimensional (1d) transform definitions, and then give the
87 straightforward extension to multi-dimensional transforms.
88 </p>
89 <table class="menu" border="0" cellspacing="0">
90 <tr><td align="left" valign="top">&bull; <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>&nbsp;&nbsp;</td><td align="left" valign="top">
91 </td></tr>
92 <tr><td align="left" valign="top">&bull; <a href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT" accesskey="2">The 1d Real-data DFT</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
93 </td></tr>
94 <tr><td align="left" valign="top">&bull; <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>&nbsp;&nbsp;</td><td align="left" valign="top">
95 </td></tr>
96 <tr><td align="left" valign="top">&bull; <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>&nbsp;&nbsp;</td><td align="left" valign="top">
97 </td></tr>
98 <tr><td align="left" valign="top">&bull; <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>&nbsp;&nbsp;</td><td align="left" valign="top">
99 </td></tr>
100 <tr><td align="left" valign="top">&bull; <a href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" accesskey="6">Multi-dimensional Transforms</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
101 </td></tr>
102 </table>
103
104
105
106
107 </body>
108 </html>