[mistercow]

This is an interesting way to visualize it, but I think the only way to really grok the Fourier transform is to use it in several different applications, and understand its role in each.

A particularly helpful tangent is to play with convolution and see the many different applications that is useful for (did you know that the shadow cast by an object is its cross section convolved with the cross section of the light source?). Once you really get convolution, and really get its relationship to the Fourier transform, you will be well along the path to enlightenment.