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Add null config files
author Chris Cannam
date Mon, 02 Mar 2020 14:03:47 +0000
parents 2cd0e3b3e1fd
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Chris@42 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
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Chris@42 6 Copyright (C) 2003 Matteo Frigo.
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Chris@42 24 <head>
Chris@42 25 <title>FFTW 3.3.5: 1d Discrete Hartley Transforms (DHTs)</title>
Chris@42 26
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Chris@42 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@42 36 <link href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" rel="up" title="What FFTW Really Computes">
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Chris@42 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@42 72 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 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>
Chris@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></a>
Chris@42 79 <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
Chris@42 80
Chris@42 81 <a name="index-discrete-Hartley-transform-2"></a>
Chris@42 82 <a name="index-DHT-1"></a>
Chris@42 83 <p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
Chris@42 84 <em>n</em> computes a real array <em>Y</em> of the same size, where:
Chris@42 85 <center><img src="equation-dht.png" align="top">.</center></p>
Chris@42 86 <a name="index-normalization-12"></a>
Chris@42 87 <p>FFTW computes an unnormalized transform, in that there is no coefficient
Chris@42 88 in front of the summation in the DHT. In other words, applying the
Chris@42 89 transform twice (the DHT is its own inverse) will multiply the input by
Chris@42 90 <em>n</em>.
Chris@42 91 </p>
Chris@42 92
Chris@42 93
Chris@42 94
Chris@42 95 </body>
Chris@42 96 </html>