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2 <head>
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3 <title>1d Discrete Hartley Transforms (DHTs) - FFTW 3.3.4</title>
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8 <link rel="up" href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes" title="What FFTW Really Computes">
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9 <link rel="prev" href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029" title="1d Real-odd DFTs (DSTs)">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.3.4, 20 September 2013).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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20 Permission is granted to make and distribute verbatim copies of
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21 this manual provided the copyright notice and this permission
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22 notice are preserved on all copies.
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23
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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45 --></style>
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46 </head>
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47 <body>
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48 <div class="node">
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49 <a name="1d-Discrete-Hartley-Transforms-(DHTs)"></a>
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50 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
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51 <p>
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52 Next: <a rel="next" accesskey="n" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a>,
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53 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>,
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54 Up: <a rel="up" accesskey="u" href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>
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55 <hr>
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56 </div>
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57
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58 <h4 class="subsection">4.8.5 1d Discrete Hartley Transforms (DHTs)</h4>
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59
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60 <p><a name="index-discrete-Hartley-transform-325"></a><a name="index-DHT-326"></a>The discrete Hartley transform (DHT) of a 1d real array X of size
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61 n computes a real array Y of the same size, where:
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62 <center><img src="equation-dht.png" align="top">.</center>
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63
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64 <p><a name="index-normalization-327"></a>FFTW computes an unnormalized transform, in that there is no coefficient
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65 in front of the summation in the DHT. In other words, applying the
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66 transform twice (the DHT is its own inverse) will multiply the input by
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67 n.
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68
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69 <!-- =========> -->
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70 </body></html>
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71
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