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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents d0c2a83c1364
children
rev   line source
Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
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Chris@82 6 Copyright (C) 2003 Matteo Frigo.
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: 1d Discrete Hartley Transforms (DHTs)</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: 1d Discrete Hartley Transforms (DHTs)">
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Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82 36 <link href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" rel="up" title="What FFTW Really Computes">
Chris@82 37 <link href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" rel="next" title="Multi-dimensional Transforms">
Chris@82 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)">
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 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>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></a>
Chris@82 78 <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
Chris@82 79
Chris@82 80 <a name="index-discrete-Hartley-transform-2"></a>
Chris@82 81 <a name="index-DHT-1"></a>
Chris@82 82 <p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
Chris@82 83 <em>n</em> computes a real array <em>Y</em> of the same size, where:
Chris@82 84 <center><img src="equation-dht.png" align="top">.</center>
Chris@82 85 </p>
Chris@82 86 <a name="index-normalization-12"></a>
Chris@82 87 <p>FFTW computes an unnormalized transform, in that there is no coefficient
Chris@82 88 in front of the summation in the DHT. In other words, applying the
Chris@82 89 transform twice (the DHT is its own inverse) will multiply the input by
Chris@82 90 <em>n</em>.
Chris@82 91 </p>
Chris@82 92
Chris@82 93
Chris@82 94
Chris@82 95 </body>
Chris@82 96 </html>