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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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3 <!-- This manual is for FFTW
4 (version 3.3.8, 24 May 2018).
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6 Copyright (C) 2003 Matteo Frigo.
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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25 <title>FFTW 3.3.8: 1d Discrete Hartley Transforms (DHTs)</title>
26
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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)">
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71 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
72 <div class="header">
73 <p>
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>
75 </div>
76 <hr>
77 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></a>
78 <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
79
80 <a name="index-discrete-Hartley-transform-2"></a>
81 <a name="index-DHT-1"></a>
82 <p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
83 <em>n</em> computes a real array <em>Y</em> of the same size, where:
84 <center><img src="equation-dht.png" align="top">.</center>
85 </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>