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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 3.2.1, 5 February 2009).
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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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47 <body>
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48 <div class="node">
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49 <p>
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50 <a name="1d-Discrete-Hartley-Transforms-(DHTs)"></a>
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51 <a name="g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029"></a>
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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-312"></a><a name="index-DHT-313"></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-314"></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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