97 lines
4.7 KiB
HTML
97 lines
4.7 KiB
HTML
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<html>
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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into another language, under the above conditions for modified versions,
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except that this permission notice may be stated in a translation
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approved by the Free Software Foundation. -->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<title>What FFTW Really Computes (FFTW 3.3.10)</title>
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<meta name="description" content="What FFTW Really Computes (FFTW 3.3.10)">
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<meta name="keywords" content="What FFTW Really Computes (FFTW 3.3.10)">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="FFTW-Reference.html" rel="up" title="FFTW Reference">
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<link href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html" rel="next" title="The 1d Discrete Fourier Transform (DFT)">
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<link href="Wisdom-Utilities.html" rel="prev" title="Wisdom Utilities">
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</style>
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</head>
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<body lang="en">
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<span id="What-FFTW-Really-Computes"></span><div class="header">
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<p>
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Previous: <a href="Wisdom.html" accesskey="p" rel="prev">Wisdom</a>, Up: <a href="FFTW-Reference.html" 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" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="What-FFTW-Really-Computes-1"></span><h3 class="section">4.8 What FFTW Really Computes</h3>
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<p>In this section, we provide precise mathematical definitions for the
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transforms that FFTW computes. These transform definitions are fairly
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standard, but some authors follow slightly different conventions for the
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normalization of the transform (the constant factor in front) and the
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sign of the complex exponent. We begin by presenting the
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one-dimensional (1d) transform definitions, and then give the
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straightforward extension to multi-dimensional transforms.
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</p>
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<table class="menu" border="0" cellspacing="0">
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<tr><td align="left" valign="top">• <a href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html" accesskey="1">The 1d Discrete Fourier Transform (DFT)</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="The-1d-Real_002ddata-DFT.html" accesskey="2">The 1d Real-data DFT</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="1d-Real_002deven-DFTs-_0028DCTs_0029.html" accesskey="3">1d Real-even DFTs (DCTs)</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html" accesskey="4">1d Real-odd DFTs (DSTs)</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html" accesskey="5">1d Discrete Hartley Transforms (DHTs)</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Multi_002ddimensional-Transforms.html" accesskey="6">Multi-dimensional Transforms</a></td><td> </td><td align="left" valign="top">
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</td></tr>
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</table>
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</body>
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</html>
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