GIFT is a piece of software developed for the practical course of the University of Oxford Physics department. It uses a Fast Fourier Transform algorithm to display the results of Fourier transforming a function, which it updates in real time. Its primary purpose is educational. It is a port/rewrite of the GIFT.app program, which was for NeXTSTEP. The current incarnation of GIFT runs on UNIX and GNU/Linux.
Download the source code, which is distributable under the terms of the BSD licence as described in the file COPYING. To build GIFT from source, you will also need the following:
Once you have everything, it's a simple case of tweaking the Makefile and running make, and make install if you wish to install GIFT.
Don't worry, it exists, but can't claim that it's too good. Get it from that link just back there. Documentation for GIFT's basic functions is in OpenOffice.org writer format. Don't have OpenOffice.org? It's available here, for no coins at all.