Mercurial > hg > sv-dependency-builds

comparison src/fftw-3.3.3/doc/html/Real_002dto_002dReal-Transform-Kinds.html @ 10:37bf6b4a2645

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add FFTW3
author Chris Cannam
date Wed, 20 Mar 2013 15:35:50 +0000
parents
children
comparison
equal deleted inserted replaced
9:c0fb53affa76 10:37bf6b4a2645
1 <html lang="en">
2 <head>
3 <title>Real-to-Real Transform Kinds - FFTW 3.3.3</title>
4 <meta http-equiv="Content-Type" content="text/html">
5 <meta name="description" content="FFTW 3.3.3">
6 <meta name="generator" content="makeinfo 4.13">
7 <link title="Top" rel="start" href="index.html#Top">
8 <link rel="up" href="Basic-Interface.html#Basic-Interface" title="Basic Interface">
9 <link rel="prev" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms" title="Real-to-Real Transforms">
10 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
11 <!--
12 This manual is for FFTW
13 (version 3.3.3, 25 November 2012).
14
15 Copyright (C) 2003 Matteo Frigo.
16
17 Copyright (C) 2003 Massachusetts Institute of Technology.
18
19 Permission is granted to make and distribute verbatim copies of
20 this manual provided the copyright notice and this permission
21 notice are preserved on all copies.
22
23 Permission is granted to copy and distribute modified versions of
24 this manual under the conditions for verbatim copying, provided
25 that the entire resulting derived work is distributed under the
26 terms of a permission notice identical to this one.
27
28 Permission is granted to copy and distribute translations of this
29 manual into another language, under the above conditions for
30 modified versions, except that this permission notice may be
31 stated in a translation approved by the Free Software Foundation.
32 -->
33 <meta http-equiv="Content-Style-Type" content="text/css">
34 <style type="text/css"><!--
35 pre.display { font-family:inherit }
36 pre.format { font-family:inherit }
37 pre.smalldisplay { font-family:inherit; font-size:smaller }
38 pre.smallformat { font-family:inherit; font-size:smaller }
39 pre.smallexample { font-size:smaller }
40 pre.smalllisp { font-size:smaller }
41 span.sc { font-variant:small-caps }
42 span.roman { font-family:serif; font-weight:normal; }
43 span.sansserif { font-family:sans-serif; font-weight:normal; }
44 --></style>
45 </head>
46 <body>
47 <div class="node">
48 <a name="Real-to-Real-Transform-Kinds"></a>
49 <a name="Real_002dto_002dReal-Transform-Kinds"></a>
50 <p>
51 Previous:&nbsp;<a rel="previous" accesskey="p" href="Real_002dto_002dReal-Transforms.html#Real_002dto_002dReal-Transforms">Real-to-Real Transforms</a>,
52 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
53 <hr>
54 </div>
55
56 <h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
57
58 <p><a name="index-kind-_0028r2r_0029-212"></a>
59 FFTW currently supports 11 different r2r transform kinds, specified by
60 one of the constants below. For the precise definitions of these
61 transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
62 introduction to these transform kinds, see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>.
63
64 <p>For dimension of size <code>n</code>, there is a corresponding &ldquo;logical&rdquo;
65 dimension <code>N</code> that determines the normalization (and the optimal
66 factorization); the formula for <code>N</code> is given for each kind below.
67 Also, with each transform kind is listed its corrsponding inverse
68 transform. FFTW computes unnormalized transforms: a transform followed
69 by its inverse will result in the original data multiplied by <code>N</code>
70 (or the product of the <code>N</code>'s for each dimension, in
71 multi-dimensions).
72 <a name="index-normalization-213"></a>
73 <ul>
74 <li><a name="index-FFTW_005fR2HC-214"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in
75 &ldquo;halfcomplex&rdquo; format, i.e. real and imaginary parts for a transform of
76 size <code>n</code> stored as:
77 <p align=center>
78 r<sub>0</sub>, r<sub>1</sub>, r<sub>2</sub>, ..., r<sub>n/2</sub>, i<sub>(n+1)/2-1</sub>, ..., i<sub>2</sub>, i<sub>1</sub>
79 </p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
80
81 <li><a name="index-FFTW_005fHC2R-215"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
82 (Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
83
84 <li><a name="index-FFTW_005fDHT-216"></a><code>FFTW_DHT</code> computes a discrete Hartley transform.
85 (Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
86 <a name="index-discrete-Hartley-transform-217"></a>
87 <li><a name="index-FFTW_005fREDFT00-218"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
88 (Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
89 <a name="index-discrete-cosine-transform-219"></a><a name="index-DCT-220"></a>
90 <li><a name="index-FFTW_005fREDFT10-221"></a><code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called &ldquo;the&rdquo; DCT).
91 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
92
93 <li><a name="index-FFTW_005fREDFT01-222"></a><code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called &ldquo;the&rdquo; IDCT, being the inverse of DCT-II).
94 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
95 <a name="index-IDCT-223"></a>
96 <li><a name="index-FFTW_005fREDFT11-224"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
97 (Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
98
99 <li><a name="index-FFTW_005fRODFT00-225"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
100 (Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
101 <a name="index-discrete-sine-transform-226"></a><a name="index-DST-227"></a>
102 <li><a name="index-FFTW_005fRODFT10-228"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
103 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
104
105 <li><a name="index-FFTW_005fRODFT01-229"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
106 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
107
108 <li><a name="index-FFTW_005fRODFT11-230"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
109 (Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
110
111 </ul>
112
113 <!-- -->
114 </body></html>
115