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Add null config files
author Chris Cannam <cannam@all-day-breakfast.com>
date Mon, 02 Mar 2020 14:03:47 +0000
parents bd3cc4d1df30
children
rev   line source
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cannam@167 3 <!-- This manual is for FFTW
cannam@167 4 (version 3.3.8, 24 May 2018).
cannam@167 5
cannam@167 6 Copyright (C) 2003 Matteo Frigo.
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cannam@167 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: 1d Discrete Hartley Transforms (DHTs)</title>
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cannam@167 37 <link href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" rel="next" title="Multi-dimensional Transforms">
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cannam@167 70 <body lang="en">
cannam@167 71 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 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>
cannam@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></a>
cannam@167 78 <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
cannam@167 79
cannam@167 80 <a name="index-discrete-Hartley-transform-2"></a>
cannam@167 81 <a name="index-DHT-1"></a>
cannam@167 82 <p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
cannam@167 83 <em>n</em> computes a real array <em>Y</em> of the same size, where:
cannam@167 84 <center><img src="equation-dht.png" align="top">.</center>
cannam@167 85 </p>
cannam@167 86 <a name="index-normalization-12"></a>
cannam@167 87 <p>FFTW computes an unnormalized transform, in that there is no coefficient
cannam@167 88 in front of the summation in the DHT. In other words, applying the
cannam@167 89 transform twice (the DHT is its own inverse) will multiply the input by
cannam@167 90 <em>n</em>.
cannam@167 91 </p>
cannam@167 92
cannam@167 93
cannam@167 94
cannam@167 95 </body>
cannam@167 96 </html>