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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>
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<a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029-1"></a>
<h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>

<a name="index-discrete-Hartley-transform-2"></a>
<a name="index-DHT-1"></a>
<p>The discrete Hartley transform (DHT) of a 1d real array <em>X</em> of size
<em>n</em> computes a real array <em>Y</em> of the same size, where:
<center><img src="equation-dht.png" align="top">.</center>
</p>
<a name="index-normalization-12"></a>
<p>FFTW computes an unnormalized transform, in that there is no coefficient
in front of the summation in the DHT.  In other words, applying the
transform twice (the DHT is its own inverse) will multiply the input by
<em>n</em>.
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author	Chris Cannam <cannam@all-day-breakfast.com>
date	Mon, 02 Mar 2020 14:03:47 +0000
parents	bd3cc4d1df30
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