|
cannam@95
|
1 <html lang="en">
|
|
cannam@95
|
2 <head>
|
|
cannam@95
|
3 <title>What FFTW Really Computes - FFTW 3.3.3</title>
|
|
cannam@95
|
4 <meta http-equiv="Content-Type" content="text/html">
|
|
cannam@95
|
5 <meta name="description" content="FFTW 3.3.3">
|
|
cannam@95
|
6 <meta name="generator" content="makeinfo 4.13">
|
|
cannam@95
|
7 <link title="Top" rel="start" href="index.html#Top">
|
|
cannam@95
|
8 <link rel="up" href="FFTW-Reference.html#FFTW-Reference" title="FFTW Reference">
|
|
cannam@95
|
9 <link rel="prev" href="Wisdom.html#Wisdom" title="Wisdom">
|
|
cannam@95
|
10 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
|
|
cannam@95
|
11 <!--
|
|
cannam@95
|
12 This manual is for FFTW
|
|
cannam@95
|
13 (version 3.3.3, 25 November 2012).
|
|
cannam@95
|
14
|
|
cannam@95
|
15 Copyright (C) 2003 Matteo Frigo.
|
|
cannam@95
|
16
|
|
cannam@95
|
17 Copyright (C) 2003 Massachusetts Institute of Technology.
|
|
cannam@95
|
18
|
|
cannam@95
|
19 Permission is granted to make and distribute verbatim copies of
|
|
cannam@95
|
20 this manual provided the copyright notice and this permission
|
|
cannam@95
|
21 notice are preserved on all copies.
|
|
cannam@95
|
22
|
|
cannam@95
|
23 Permission is granted to copy and distribute modified versions of
|
|
cannam@95
|
24 this manual under the conditions for verbatim copying, provided
|
|
cannam@95
|
25 that the entire resulting derived work is distributed under the
|
|
cannam@95
|
26 terms of a permission notice identical to this one.
|
|
cannam@95
|
27
|
|
cannam@95
|
28 Permission is granted to copy and distribute translations of this
|
|
cannam@95
|
29 manual into another language, under the above conditions for
|
|
cannam@95
|
30 modified versions, except that this permission notice may be
|
|
cannam@95
|
31 stated in a translation approved by the Free Software Foundation.
|
|
cannam@95
|
32 -->
|
|
cannam@95
|
33 <meta http-equiv="Content-Style-Type" content="text/css">
|
|
cannam@95
|
34 <style type="text/css"><!--
|
|
cannam@95
|
35 pre.display { font-family:inherit }
|
|
cannam@95
|
36 pre.format { font-family:inherit }
|
|
cannam@95
|
37 pre.smalldisplay { font-family:inherit; font-size:smaller }
|
|
cannam@95
|
38 pre.smallformat { font-family:inherit; font-size:smaller }
|
|
cannam@95
|
39 pre.smallexample { font-size:smaller }
|
|
cannam@95
|
40 pre.smalllisp { font-size:smaller }
|
|
cannam@95
|
41 span.sc { font-variant:small-caps }
|
|
cannam@95
|
42 span.roman { font-family:serif; font-weight:normal; }
|
|
cannam@95
|
43 span.sansserif { font-family:sans-serif; font-weight:normal; }
|
|
cannam@95
|
44 --></style>
|
|
cannam@95
|
45 </head>
|
|
cannam@95
|
46 <body>
|
|
cannam@95
|
47 <div class="node">
|
|
cannam@95
|
48 <a name="What-FFTW-Really-Computes"></a>
|
|
cannam@95
|
49 <p>
|
|
cannam@95
|
50 Previous: <a rel="previous" accesskey="p" href="Wisdom.html#Wisdom">Wisdom</a>,
|
|
cannam@95
|
51 Up: <a rel="up" accesskey="u" href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>
|
|
cannam@95
|
52 <hr>
|
|
cannam@95
|
53 </div>
|
|
cannam@95
|
54
|
|
cannam@95
|
55 <h3 class="section">4.8 What FFTW Really Computes</h3>
|
|
cannam@95
|
56
|
|
cannam@95
|
57 <p>In this section, we provide precise mathematical definitions for the
|
|
cannam@95
|
58 transforms that FFTW computes. These transform definitions are fairly
|
|
cannam@95
|
59 standard, but some authors follow slightly different conventions for the
|
|
cannam@95
|
60 normalization of the transform (the constant factor in front) and the
|
|
cannam@95
|
61 sign of the complex exponent. We begin by presenting the
|
|
cannam@95
|
62 one-dimensional (1d) transform definitions, and then give the
|
|
cannam@95
|
63 straightforward extension to multi-dimensional transforms.
|
|
cannam@95
|
64
|
|
cannam@95
|
65 <ul class="menu">
|
|
cannam@95
|
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>
|
|
cannam@95
|
67 <li><a accesskey="2" href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT">The 1d Real-data DFT</a>
|
|
cannam@95
|
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>
|
|
cannam@95
|
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>
|
|
cannam@95
|
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>
|
|
cannam@95
|
71 <li><a accesskey="6" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a>
|
|
cannam@95
|
72 </ul>
|
|
cannam@95
|
73
|
|
cannam@95
|
74 <!-- =========> -->
|
|
cannam@95
|
75 </body></html>
|
|
cannam@95
|
76
|
