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3 <title>What FFTW Really Computes - FFTW 3.2.1</title>
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55 <h3 class="section">4.8 What FFTW Really Computes</h3>
56
57 <p>In this section, we provide precise mathematical definitions for the
58 transforms that FFTW computes. These transform definitions are fairly
59 standard, but some authors follow slightly different conventions for the
60 normalization of the transform (the constant factor in front) and the
61 sign of the complex exponent. We begin by presenting the
62 one-dimensional (1d) transform definitions, and then give the
63 straightforward extension to multi-dimensional transforms.
64
65 <ul class="menu">
66 <li><a accesskey="1" href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029">The 1d Discrete Fourier Transform (DFT)</a>
67 <li><a accesskey="2" href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT">The 1d Real-data DFT</a>
68 <li><a accesskey="3" href="1d-Real_002deven-DFTs-_0028DCTs_0029.html#g_t1d-Real_002deven-DFTs-_0028DCTs_0029">1d Real-even DFTs (DCTs)</a>
69 <li><a accesskey="4" href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029">1d Real-odd DFTs (DSTs)</a>
70 <li><a accesskey="5" href="1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html#g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029">1d Discrete Hartley Transforms (DHTs)</a>
71 <li><a accesskey="6" href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms">Multi-dimensional Transforms</a>
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