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cannam@167: <title>FFTW 3.3.8: What FFTW Really Computes</title>
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cannam@167: <link href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029" rel="next" title="The 1d Discrete Fourier Transform (DFT)">
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cannam@167: Previous: <a href="Wisdom.html#Wisdom" accesskey="p" rel="prev">Wisdom</a>, Up: <a href="FFTW-Reference.html#FFTW-Reference" accesskey="u" rel="up">FFTW Reference</a> [<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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cannam@167: <h3 class="section">4.8 What FFTW Really Computes</h3>
cannam@167:
cannam@167: <p>In this section, we provide precise mathematical definitions for the
cannam@167: transforms that FFTW computes. These transform definitions are fairly
cannam@167: standard, but some authors follow slightly different conventions for the
cannam@167: normalization of the transform (the constant factor in front) and the
cannam@167: sign of the complex exponent. We begin by presenting the
cannam@167: one-dimensional (1d) transform definitions, and then give the
cannam@167: straightforward extension to multi-dimensional transforms.
cannam@167: </p>
cannam@167: <table class="menu" border="0" cellspacing="0">
cannam@167: <tr><td align="left" valign="top">• <a href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029" accesskey="1">The 1d Discrete Fourier Transform (DFT)</a>:</td><td> </td><td align="left" valign="top">
cannam@167: </td></tr>
cannam@167: <tr><td align="left" valign="top">• <a href="The-1d-Real_002ddata-DFT.html#The-1d-Real_002ddata-DFT" accesskey="2">The 1d Real-data DFT</a>:</td><td> </td><td align="left" valign="top">
cannam@167: </td></tr>
cannam@167: <tr><td align="left" valign="top">• <a href="1d-Real_002deven-DFTs-_0028DCTs_0029.html#g_t1d-Real_002deven-DFTs-_0028DCTs_0029" accesskey="3">1d Real-even DFTs (DCTs)</a>:</td><td> </td><td align="left" valign="top">
cannam@167: </td></tr>
cannam@167: <tr><td align="left" valign="top">• <a href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html#g_t1d-Real_002dodd-DFTs-_0028DSTs_0029" accesskey="4">1d Real-odd DFTs (DSTs)</a>:</td><td> </td><td align="left" valign="top">
cannam@167: </td></tr>
cannam@167: <tr><td align="left" valign="top">• <a href="1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html#g_t1d-Discrete-Hartley-Transforms-_0028DHTs_0029" accesskey="5">1d Discrete Hartley Transforms (DHTs)</a>:</td><td> </td><td align="left" valign="top">
cannam@167: </td></tr>
cannam@167: <tr><td align="left" valign="top">• <a href="Multi_002ddimensional-Transforms.html#Multi_002ddimensional-Transforms" accesskey="6">Multi-dimensional Transforms</a>:</td><td> </td><td align="left" valign="top">
cannam@167: </td></tr>
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