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<title>GNU Scientific Library &ndash; Reference Manual: Fast Fourier Transforms</title>

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<p>
Next: <a href="Numerical-Integration.html#Numerical-Integration" accesskey="n" rel="next">Numerical Integration</a>, Previous: <a href="Eigensystems.html#Eigensystems" accesskey="p" rel="previous">Eigensystems</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Fast-Fourier-Transforms-_0028FFTs_0029"></a>
<h2 class="chapter">16 Fast Fourier Transforms (FFTs)</h2>
<a name="index-FFT"></a>
<a name="index-Fast-Fourier-Transforms_002c-see-FFT"></a>
<a name="index-Fourier-Transforms_002c-see-FFT"></a>
<a name="index-Discrete-Fourier-Transforms_002c-see-FFT"></a>
<a name="index-DFTs_002c-see-FFT"></a>

<p>This chapter describes functions for performing Fast Fourier Transforms
(FFTs).  The library includes radix-2 routines (for lengths which are a
power of two) and mixed-radix routines (which work for any length).  For
efficiency there are separate versions of the routines for real data and
for complex data.  The mixed-radix routines are a reimplementation of the
<small>FFTPACK</small> library of Paul Swarztrauber.  Fortran code for <small>FFTPACK</small> is
available on Netlib (<small>FFTPACK</small> also includes some routines for sine and
cosine transforms but these are currently not available in GSL).  For
details and derivations of the underlying algorithms consult the
document <cite>GSL FFT Algorithms</cite> (see <a href="FFT-References-and-Further-Reading.html#FFT-References-and-Further-Reading">FFT References and Further Reading</a>)
</p>
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<tr><td align="left" valign="top">&bull; <a href="Mathematical-Definitions.html#Mathematical-Definitions" accesskey="1">Mathematical Definitions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Overview-of-complex-data-FFTs.html#Overview-of-complex-data-FFTs" accesskey="2">Overview of complex data FFTs</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Radix_002d2-FFT-routines-for-complex-data.html#Radix_002d2-FFT-routines-for-complex-data" accesskey="3">Radix-2 FFT routines for complex data</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Mixed_002dradix-FFT-routines-for-complex-data.html#Mixed_002dradix-FFT-routines-for-complex-data" accesskey="4">Mixed-radix FFT routines for complex data</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Overview-of-real-data-FFTs.html#Overview-of-real-data-FFTs" accesskey="5">Overview of real data FFTs</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Radix_002d2-FFT-routines-for-real-data.html#Radix_002d2-FFT-routines-for-real-data" accesskey="6">Radix-2 FFT routines for real data</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Mixed_002dradix-FFT-routines-for-real-data.html#Mixed_002dradix-FFT-routines-for-real-data" accesskey="7">Mixed-radix FFT routines for real data</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="FFT-References-and-Further-Reading.html#FFT-References-and-Further-Reading" accesskey="8">FFT References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
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