What is the most common library for FFT?
FFTW is the most popular FFT library. It has planty of features and it's often used as the reference point, but a number of other libraries has comparable or better performance.
What is fftw3f?
FFTW is a subroutine library written in C for computing the Discrete Fourier Transform in one or more dimensions, of both real and complex data, of arbitrary input size.