# Fast Fourier Transforms (FFTs)

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 FFTPACK library by Paul Swarztrauber. Fortran code for FFTPACK is available on Netlib (FFTPACK 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 GSL FFT Algorithms (see section References and Further Reading)

- Mathematical Definitions
- Overview of complex data FFTs
- Radix-2 FFT routines for complex data
- Mixed-radix FFT routines for complex data
- Overview of real data FFTs
- Radix-2 FFT routines for real data
- Mixed-radix FFT routines for real data
- FFT References and Further Reading