Despite its curious name, Fast Fourier Transform in the West (FFTW) is a powerful, free "C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of both real and complex data, and of arbitrary input size." Developed by researchers from the Massachusetts Institute of Technology, FFTW purportedly has outstanding performance when compared with other DFT algorithms. This statement is supported by experimental results from extensive speed and accuracy benchmarks. FFTW can be downloaded directly from this site, along with substantial documentation and three research papers stemming from its development.