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85 lines
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85 lines
3.8 KiB
HTML
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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preserved on all copies.
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Permission is granted to copy and distribute modified versions of this
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manual under the conditions for verbatim copying, provided that the
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entire resulting derived work is distributed under the terms of a
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permission notice identical to this one.
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Permission is granted to copy and distribute translations of this manual
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into another language, under the above conditions for modified versions,
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except that this permission notice may be stated in a translation
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approved by the Free Software Foundation. -->
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<title>1d Discrete Hartley Transforms (DHTs) (FFTW 3.3.10)</title>
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="What-FFTW-Really-Computes.html" rel="up" title="What FFTW Really Computes">
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<link href="Multi_002ddimensional-Transforms.html" rel="next" title="Multi-dimensional Transforms">
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<link href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html" rel="prev" title="1d Real-odd DFTs (DSTs)">
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<span id="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></span><div class="header">
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<p>
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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>
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</div>
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<hr>
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<span id="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></span><h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
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<span id="index-discrete-Hartley-transform-2"></span>
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<span id="index-DHT-1"></span>
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<p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
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<em>n</em> computes a real array <em>Y</em> of the same size, where:
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<center><img src="equation-dht.png" align="top">.</center>
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</p>
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<span id="index-normalization-12"></span>
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<p>FFTW computes an unnormalized transform, in that there is no coefficient
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in front of the summation in the DHT. In other words, applying the
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transform twice (the DHT is its own inverse) will multiply the input by
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<em>n</em>.
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</p>
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