86 lines
3.8 KiB
HTML
86 lines
3.8 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>1d Discrete Hartley Transforms (DHTs) (FFTW 3.3.10)</title>
|
||
|
|
|
||
|
|
<meta name="description" content="1d Discrete Hartley Transforms (DHTs) (FFTW 3.3.10)">
|
||
|
|
<meta name="keywords" content="1d Discrete Hartley Transforms (DHTs) (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="What-FFTW-Really-Computes.html" rel="up" title="What FFTW Really Computes">
|
||
|
|
<link href="Multi_002ddimensional-Transforms.html" rel="next" title="Multi-dimensional Transforms">
|
||
|
|
<link href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html" rel="prev" title="1d Real-odd DFTs (DSTs)">
|
||
|
|
<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="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></span><div class="header">
|
||
|
|
<p>
|
||
|
|
Next: <a href="Multi_002ddimensional-Transforms.html" accesskey="n" rel="next">Multi-dimensional Transforms</a>, Previous: <a href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html" accesskey="p" rel="prev">1d Real-odd DFTs (DSTs)</a>, Up: <a href="What-FFTW-Really-Computes.html" accesskey="u" rel="up">What FFTW Really Computes</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="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></span><h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
|
||
|
|
|
||
|
|
<span id="index-discrete-Hartley-transform-2"></span>
|
||
|
|
<span id="index-DHT-1"></span>
|
||
|
|
<p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
|
||
|
|
<em>n</em> computes a real array <em>Y</em> of the same size, where:
|
||
|
|
<center><img src="equation-dht.png" align="top">.</center>
|
||
|
|
</p>
|
||
|
|
<span id="index-normalization-12"></span>
|
||
|
|
<p>FFTW computes an unnormalized transform, in that there is no coefficient
|
||
|
|
in front of the summation in the DHT. In other words, applying the
|
||
|
|
transform twice (the DHT is its own inverse) will multiply the input by
|
||
|
|
<em>n</em>.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</body>
|
||
|
|
</html>
|