I have really been struggling with the concepts involved with the Fourier analysis technique for the past few days. Has anyone got a more laymens explanation to the transformation process? Eventually, I would like to understand the more advanced Fast Fourier Transform, too, but I'm trying to grasp one level at a time! So far, all I get is that the Fourier approach is a specialized wavelet analysis technique which allows one to store time-domain data in more compact structures, as well as revealing more precise information about the wave, it's frequencies, phases, etc.

I also understand that it is based on a complex number algorithm, and those numbers in some way relate to the sin and cosines of the packet.

All I can get from the FFT is that it is hundreds of times more efficient than calculating each number linearly, and is implemented by somehow feeding previous calculations into current calculations, and that it is often described with "butterfly" graphs (which are a complete mystery to me).

My goal, using the different FFT transformations, is to project sound waves that I have captured from my sound card onto graphs on screen.