[Rich Wong]

Originally Posted by Mike Betts

From my increasingly faulty memory, the FT and IFT (Inverse FT) are unique whereas the FFT (Fast FT) and IFFT (inverse FFT) may not be.

The algorithm you have outlined will probably not work. Nice try though...

The FFT uses a "butterfly" algorithm which lends itself well to computers.

I'm not sure how to attack the DFT (discrete FT) without talking about continuous and discrete domains... This gets messy fast...

FFT are easy to implement with DSP ICs or programming. One of my pass engineering job was to used the these ICs to execute 10x10 FFT for a spread spectrum project. We choose hardware because of the "Need for Speed!"
It was the most fun I ever had with engineering, programming and math.