FFTW is a C
subroutine library for computing the discrete Fourier transform (DFT)
in one or more dimensions, of arbitrary input size, and of both real
and complex data (as well as of even/odd data, i.e. the discrete
cosine/sine transforms or DCT/DST). We believe that FFTW,
which is free software, should become the FFT library of choice for most
The latest official release of FFTW is version 3.3.9,
available from our download page. Version
3.3 introduced support for the AVX x86 extensions, a
distributed-memory implementation on top of MPI, and a Fortran 2003
API. Version 3.3.1 introduced support for the ARM Neon
extensions. See the release notes for
The FFTW package was developed at MIT by Matteo Frigo and Steven G. Johnson.
performed on on a variety of platforms, show that FFTW's performance
is typically superior to that of other publicly available FFT
software, and is even competitive with vendor-tuned codes. In
contrast to vendor-tuned codes, however, FFTW's performance is
portable: the same program will perform well on most
architectures without modification. Hence the name, "FFTW," which
stands for the somewhat whimsical title of "Fastest Fourier
Transform in the West."
mailing list to receive release announcements (or use the web feed ).
FFTW 3.3.9 is the latest official version of FFTW (refer to the release notes to find out what is new).
Here is a list of some of FFTW's more interesting features:
- Speed. (Supports SSE/SSE2/Altivec, since version
3.0. Version 3.3.1 supports AVX and ARM Neon.)
- Both one-dimensional and multi-dimensional transforms.
- Arbitrary-size transforms. (Sizes with small prime factors are
best, but FFTW uses O(N log N) algorithms even for prime sizes.)
- Fast transforms of purely real input or output data.
- Transforms of real even/odd data: the discrete cosine transform
(DCT) and the discrete sine transform (DST), types I-IV. (Version 3.0 or later.)
- Efficient handling of multiple, strided transforms. (This lets you
do things like transform multiple arrays at once, transform one
dimension of a multi-dimensional array, or transform one field of a
- Parallel transforms: parallelized
code for platforms with SMP machines with some flavor
(e.g. POSIX) or OpenMP. An MPI version for distributed-memory transforms is
also available in FFTW 3.3.
- Portable to any platform with a C compiler.
- Documentation in HTML and other formats.
- Both C and Fortran interfaces.
software, released under the GNU General Public License (GPL, see FFTW license).
(Non-free licenses may also be purchased from MIT, for users who do not want their programs protected by
the GPL. Contact us for details.) (See also the FAQ.)
If you are still using
FFTW 2.x, please note that FFTW 2.x was last updated in 1999
and it is obsolete. Please upgrade to FFTW 3.x. The API of FFTW 3.x
is incompatible with that of FFTW 2.x, for reasons of
performance and generality (see
First, read the FFTW Frequently Asked Questions
Manual: HTML or PDF.
the fftw-wisdom and fftw-wisdom-to-conf utilities.
For general questions about Fourier transforms, see our links to FFT-related resources. People often ask
us how to compute a subset of the FFT outputs, so we have posted a
short discussion of pruned FFTs.
We benchmarked FFTW against many other FFT programs, in one to
three dimensions, on a variety of platforms. You can view the results
from this benchmark, or download it to run on your own machine and
compiler, at the benchFFT web
An audio interview of the FFTW authors is available from the RCE podcast program.
Versions 3.3.9 and 2.1.5 of FFTW may be downloaded from this site. Feel free to post
FFTW on your own site, but be sure to tell us so that we can link to
your page and notify you of updates to the software.
- BibTeX file of FFTW references.
- The most current general paper about FFTW, and the preferred FFTW
reference: Matteo Frigo and Steven G. Johnson,
"The Design and Implementation of
FFTW3," Proceedings of the IEEE 93 (2),
216–231 (2005). Invited paper, Special Issue on Program
Generation, Optimization, and Platform Adaptation. [Link is to
our preprint of published article; also
in Postscript. Official issue
FFTs in Practice, our chapter in the online book Fast Fourier
Transforms edited by C. S. Burrus.
- "A Fast Fourier Transform Compiler," by
Matteo Frigo, in the Proceedings of the 1999 ACM SIGPLAN Conference on
Programming Language Design and Implementation
(PLDI '99), Atlanta,
Georgia, May 1999. This paper describes the guts of the FFTW codelet
generator. (Also in Postscript.
The slides from the talk are also
- An earlier (and somewhat out of date) paper on FFTW was published
in the 1998 ICASSP conference proceedings (vol. 3, pp. 1381-1384) with
the title "FFTW: An Adaptive Software
Architecture for the FFT" (also in Postscript), by M. Frigo and
S. G. Johnson.
- An even older technical report is "The Fastest Fourier Transform in the West,"
MIT-LCS-TR-728 (September 1997) (also in Postscript.).
- You might also be interested in "Cache-Oblivious
Algorithms," by M. Frigo, C. E. Leiserson, H. Prokop, and
S. Ramachandran (FOCS '99).
- The slides from the 7/28/98 talk
"The Fastest Fourier Transform in the West," by M. Frigo, are also
available, along with the slides from
a shorter 1/14/98 talk on the same subject by S. G. Johnson.
- A paper on a new FFT algorithm that, following James Van Buskirk,
improves upon previous records for the arithmetic complexity of the
DFT and related transforms, is: Steven G. Johnson and Matteo Frigo,
"A modified split-radix FFT with fewer
arithmetic operations", IEEE Trans. Signal Processing
55 (1), 111–119 (2007). Two preprints describing the
application of the new algorithm to discrete cosine transforms are
DCT/DST algorithms with reduced number of arithmetic operations"
(March 2007) and "Type-IV
DCT, DST, and MDCT algorithms with reduced numbers of arithmetic
operations" (August 2007), by X. Shao and S. G. Johnson.
J. H. Wilkinson Prize for Numerical Software, which is awarded
every four years to the software that "best addresses all phases of
the preparation of high quality numerical software." Wilkinson was a
seminal figure in modern numerical analysis as well as a key proponent
of the notion of reusable, common libraries for scientific computing,
and we are especially honored to receive this award in his memory.
Our paper "A Fast Fourier Transform Compiler" (in PLDI 1999) received
the Most Influential PLDI Paper award in 2009.
We are grateful for the support of many people and companies,
including Sun, Intel, the GNU project, and the Linux community.
Please see the acknowledgements
section of our manual for a more complete list of those who helped
us. We are especially thankful to all of our users for their
continuing support, feedback, and interest in the development of FFTW.
We have put together a list of links to other
interesting sites with FFT-related code or information. This should
be helpful if you want to know more about Fourier transforms or if for
some reason FFTW doesn't satisfy your needs.
If you have comments, questions, or suggestions regarding FFTW, don't
hesitate to email us at firstname.lastname@example.org.
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