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Add FFTW3
author | Chris Cannam |
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date | Wed, 20 Mar 2013 15:35:50 +0000 |
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<html lang="en"> <head> <title>1d Discrete Hartley Transforms (DHTs) - FFTW 3.3.3</title> <meta http-equiv="Content-Type" content="text/html"> <meta name="description" content="FFTW 3.3.3"> <meta name="generator" content="makeinfo 4.13"> <link title="Top" rel="start" href="index.html#Top"> <link rel="up" href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" title="What FFTW Really Computes"> <link rel="prev" href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029" title="1d Real-odd DFTs (DSTs)"> <link rel="next" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" title="Multi-dimensional Transforms"> <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> <!-- This manual is for FFTW (version 3.3.3, 25 November 2012). Copyright (C) 2003 Matteo Frigo. Copyright (C) 2003 Massachusetts Institute of Technology. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the Free Software Foundation. --> <meta http-equiv="Content-Style-Type" content="text/css"> <style type="text/css"><!-- pre.display { font-family:inherit } pre.format { font-family:inherit } pre.smalldisplay { font-family:inherit; font-size:smaller } pre.smallformat { font-family:inherit; font-size:smaller } pre.smallexample { font-size:smaller } pre.smalllisp { font-size:smaller } span.sc { font-variant:small-caps } span.roman { font-family:serif; font-weight:normal; } span.sansserif { font-family:sans-serif; font-weight:normal; } --></style> </head> <body> <div class="node"> <a name="1d-Discrete-Hartley-Transforms-(DHTs)"></a> <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a> <p> Next: <a rel="next" accesskey="n" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a>, Previous: <a rel="previous" accesskey="p" href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029">1d Real-odd DFTs (DSTs)</a>, Up: <a rel="up" accesskey="u" href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a> <hr> </div> <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4> <p><a name="index-discrete-Hartley-transform-322"></a><a name="index-DHT-323"></a>The discrete Hartley transform (DHT) of a 1d real array X of size n computes a real array Y of the same size, where: <center><img src="equation-dht.png" align="top">.</center> <p><a name="index-normalization-324"></a>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 n. <!-- =========> --> </body></html>