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<title>Fast Fourier Transforms - GNU Scientific Library -- Reference Manual</title>
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<h2 class="chapter">15 Fast Fourier Transforms (FFTs)</h2>
<p><a name="index-FFT-1390"></a><a name="index-Fast-Fourier-Transforms_002c-see-FFT-1391"></a><a name="index-Fourier-Transforms_002c-see-FFT-1392"></a><a name="index-Discrete-Fourier-Transforms_002c-see-FFT-1393"></a><a name="index-DFTs_002c-see-FFT-1394"></a>
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
<span class="sc">fftpack</span> library of Paul Swarztrauber. Fortran code for <span class="sc">fftpack</span> is
available on Netlib (<span class="sc">fftpack</span> 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</a>)
<ul class="menu">
<li><a accesskey="1" href="Mathematical-Definitions.html">Mathematical Definitions</a>
<li><a accesskey="2" href="Overview-of-complex-data-FFTs.html">Overview of complex data FFTs</a>
<li><a accesskey="3" href="Radix_002d2-FFT-routines-for-complex-data.html">Radix-2 FFT routines for complex data</a>
<li><a accesskey="4" href="Mixed_002dradix-FFT-routines-for-complex-data.html">Mixed-radix FFT routines for complex data</a>
<li><a accesskey="5" href="Overview-of-real-data-FFTs.html">Overview of real data FFTs</a>
<li><a accesskey="6" href="Radix_002d2-FFT-routines-for-real-data.html">Radix-2 FFT routines for real data</a>
<li><a accesskey="7" href="Mixed_002dradix-FFT-routines-for-real-data.html">Mixed-radix FFT routines for real data</a>
<li><a accesskey="8" href="FFT-References-and-Further-Reading.html">FFT References and Further Reading</a>
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