Fourier transform

I'm really dumb and I have to have a basic understanding of a Fourier transform.

The basic idea is that you can express any function f(x) as an infinite sum of sine and cosine waves of varying frequencies. The Fourier transform takes f(x) and produces a new function, F(k), where k is a spatial frequency. F(k) is related to the amplitude of a sine wave at spatial frequency k.