Mercurial > hg > sv-dependency-builds

comparison src/fftw-3.3.5/doc/html/1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html @ 42:2cd0e3b3e1fd

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
parents
children
comparison
equal deleted inserted replaced
41:481f5f8c5634 42:2cd0e3b3e1fd
1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
2 <html>
3 <!-- This manual is for FFTW
4 (version 3.3.5, 30 July 2016).
5
6 Copyright (C) 2003 Matteo Frigo.
7
8 Copyright (C) 2003 Massachusetts Institute of Technology.
9
10 Permission is granted to make and distribute verbatim copies of this
11 manual provided the copyright notice and this permission notice are
12 preserved on all copies.
13
14 Permission is granted to copy and distribute modified versions of this
15 manual under the conditions for verbatim copying, provided that the
16 entire resulting derived work is distributed under the terms of a
17 permission notice identical to this one.
18
19 Permission is granted to copy and distribute translations of this manual
20 into another language, under the above conditions for modified versions,
21 except that this permission notice may be stated in a translation
22 approved by the Free Software Foundation. -->
23 <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
24 <head>
25 <title>FFTW 3.3.5: 1d Discrete Hartley Transforms (DHTs)</title>
26
27 <meta name="description" content="FFTW 3.3.5: 1d Discrete Hartley Transforms (DHTs)">
28 <meta name="keywords" content="FFTW 3.3.5: 1d Discrete Hartley Transforms (DHTs)">
29 <meta name="resource-type" content="document">
30 <meta name="distribution" content="global">
31 <meta name="Generator" content="makeinfo">
32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
33 <link href="index.html#Top" rel="start" title="Top">
34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
36 <link href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" rel="up" title="What FFTW Really Computes">
37 <link href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" rel="next" title="Multi-dimensional Transforms">
38 <link href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029" rel="prev" title="1d Real-odd DFTs (DSTs)">
39 <style type="text/css">
40 <!--
41 a.summary-letter {text-decoration: none}
42 blockquote.smallquotation {font-size: smaller}
43 div.display {margin-left: 3.2em}
44 div.example {margin-left: 3.2em}
45 div.indentedblock {margin-left: 3.2em}
46 div.lisp {margin-left: 3.2em}
47 div.smalldisplay {margin-left: 3.2em}
48 div.smallexample {margin-left: 3.2em}
49 div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
50 div.smalllisp {margin-left: 3.2em}
51 kbd {font-style:oblique}
52 pre.display {font-family: inherit}
53 pre.format {font-family: inherit}
54 pre.menu-comment {font-family: serif}
55 pre.menu-preformatted {font-family: serif}
56 pre.smalldisplay {font-family: inherit; font-size: smaller}
57 pre.smallexample {font-size: smaller}
58 pre.smallformat {font-family: inherit; font-size: smaller}
59 pre.smalllisp {font-size: smaller}
60 span.nocodebreak {white-space:nowrap}
61 span.nolinebreak {white-space:nowrap}
62 span.roman {font-family:serif; font-weight:normal}
63 span.sansserif {font-family:sans-serif; font-weight:normal}
64 ul.no-bullet {list-style: none}
65 -->
66 </style>
67
68
69 </head>
70
71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
72 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
73 <div class="header">
74 <p>
75 Next: <a href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" accesskey="n" rel="next">Multi-dimensional Transforms</a>, Previous: <a href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029" accesskey="p" rel="prev">1d Real-odd DFTs (DSTs)</a>, Up: <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" accesskey="u" rel="up">What FFTW Really Computes</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="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></a>
79 <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
80
81 <a name="index-discrete-Hartley-transform-2"></a>
82 <a name="index-DHT-1"></a>
83 <p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
84 <em>n</em> computes a real array <em>Y</em> of the same size, where:
85 <center><img src="equation-dht.png" align="top">.</center></p>
86 <a name="index-normalization-12"></a>
87 <p>FFTW computes an unnormalized transform, in that there is no coefficient
88 in front of the summation in the DHT. In other words, applying the
89 transform twice (the DHT is its own inverse) will multiply the input by
90 <em>n</em>.
91 </p>
92
93
94
95 </body>
96 </html>