FFTW is
C subroutine library, available for free, that when used with a program allows it to do
Discrete Fourier Transforms(DFT). The FFTW package was developed by Matteo Frigo and Steven G. Johnson at
MIT, with the intent of being a preferred FFT library for scientists and interested programmers. The library has won awards for usefulness and speed.
The Name
FFTW stands for "The Fastest Fourier Transform in the West" which is a tongue in cheek reference to gunslingers in the Old West. One might point out that MIT is nowhere near the Western US and is in fact on the East Coast, in fact its not very west at all, to which Frigo will reply "not to an Italian."
The Purpose
FFTW is meant as an open-source solution to FFT needs for anyone who wants to implement it. Matlab uses FFTW for its FFT needs and it is at the same time an optimal implementation of FFT, providing O(nLog(n)) runtime for large(prime) data sets and is capable multidimensional work. Being so featured it took the J. H. Wilkinson Prize for Numerical software. Furthermore, FFTW is written in ANSI C, so that it is easily portable to any computer and no other language cannot boast the same(With the exception of Java, which is generally unsuited for numerical computation).
FFTW is a useful tool for any scientist or engineer who needs to process some sort of signal data and considers the time spent writing a program to run the library on a set of data worth the money spent buying a program that has already been written, such as Matlab. This FFT performs better in a number of ways compared to other FFTs, according to the benchmarks on their site. FFTW generally performs more accurately, but with the same level of precision, than most of the other FFTs they tested. If you are a hacker with a scientific bent or a scientist who can allocate or de-allocate memory successfully, I recommend this library for numerous research applications.
The Website
http://www.fftw.org/