Fourier Transforms are used to move into the frequency domain where many Digital Signal Processing techniques can be used. The FFT or Fast Fourier Transform is usually the practical implementation of a Fourier transform. This technique can be used on a DSP processor like the C6000, or implemented in hardware such as an FPGA.
The Xilinx Core Generator that is part of the standard FPGA development tools provides FFT functions. We offer an FFT demo/framework that shows you how to use that. It can perform a 256 point FFT in 1.7us! We also have a VHDL version that you can use if you prefer.
You can also implement FFTs with C6000 DSPs.