mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-06 04:45:05 +00:00
96 lines
4.7 KiB
HTML
96 lines
4.7 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
|
|
<html>
|
|
<!-- This manual is for FFTW
|
|
(version 3.3.10, 10 December 2020).
|
|
|
|
Copyright (C) 2003 Matteo Frigo.
|
|
|
|
Copyright (C) 2003 Massachusetts Institute of Technology.
|
|
|
|
Permission is granted to make and distribute verbatim copies of this
|
|
manual provided the copyright notice and this permission notice are
|
|
preserved on all copies.
|
|
|
|
Permission is granted to copy and distribute modified versions of this
|
|
manual under the conditions for verbatim copying, provided that the
|
|
entire resulting derived work is distributed under the terms of a
|
|
permission notice identical to this one.
|
|
|
|
Permission is granted to copy and distribute translations of this manual
|
|
into another language, under the above conditions for modified versions,
|
|
except that this permission notice may be stated in a translation
|
|
approved by the Free Software Foundation. -->
|
|
<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ -->
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
|
|
<title>What FFTW Really Computes (FFTW 3.3.10)</title>
|
|
|
|
<meta name="description" content="What FFTW Really Computes (FFTW 3.3.10)">
|
|
<meta name="keywords" content="What FFTW Really Computes (FFTW 3.3.10)">
|
|
<meta name="resource-type" content="document">
|
|
<meta name="distribution" content="global">
|
|
<meta name="Generator" content="makeinfo">
|
|
<link href="index.html" rel="start" title="Top">
|
|
<link href="Concept-Index.html" rel="index" title="Concept Index">
|
|
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
|
|
<link href="FFTW-Reference.html" rel="up" title="FFTW Reference">
|
|
<link href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html" rel="next" title="The 1d Discrete Fourier Transform (DFT)">
|
|
<link href="Wisdom-Utilities.html" rel="prev" title="Wisdom Utilities">
|
|
<style type="text/css">
|
|
<!--
|
|
a.summary-letter {text-decoration: none}
|
|
blockquote.indentedblock {margin-right: 0em}
|
|
div.display {margin-left: 3.2em}
|
|
div.example {margin-left: 3.2em}
|
|
div.lisp {margin-left: 3.2em}
|
|
kbd {font-style: oblique}
|
|
pre.display {font-family: inherit}
|
|
pre.format {font-family: inherit}
|
|
pre.menu-comment {font-family: serif}
|
|
pre.menu-preformatted {font-family: serif}
|
|
span.nolinebreak {white-space: nowrap}
|
|
span.roman {font-family: initial; font-weight: normal}
|
|
span.sansserif {font-family: sans-serif; font-weight: normal}
|
|
ul.no-bullet {list-style: none}
|
|
-->
|
|
</style>
|
|
|
|
|
|
</head>
|
|
|
|
<body lang="en">
|
|
<span id="What-FFTW-Really-Computes"></span><div class="header">
|
|
<p>
|
|
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>
|
|
</div>
|
|
<hr>
|
|
<span id="What-FFTW-Really-Computes-1"></span><h3 class="section">4.8 What FFTW Really Computes</h3>
|
|
|
|
<p>In this section, we provide precise mathematical definitions for the
|
|
transforms that FFTW computes. These transform definitions are fairly
|
|
standard, but some authors follow slightly different conventions for the
|
|
normalization of the transform (the constant factor in front) and the
|
|
sign of the complex exponent. We begin by presenting the
|
|
one-dimensional (1d) transform definitions, and then give the
|
|
straightforward extension to multi-dimensional transforms.
|
|
</p>
|
|
<table class="menu" border="0" cellspacing="0">
|
|
<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">
|
|
</td></tr>
|
|
<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">
|
|
</td></tr>
|
|
<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">
|
|
</td></tr>
|
|
<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">
|
|
</td></tr>
|
|
<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">
|
|
</td></tr>
|
|
<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">
|
|
</td></tr>
|
|
</table>
|
|
|
|
|
|
|
|
|
|
</body>
|
|
</html>
|