FFT stands for Fast Fourier Transform. It is the only one of several Fourier Transforms we will use here, but let's drop the "fast" for a moment and talk about the Fourier Transform first. We have talked a lot about spectra and frequencies, but have mainly stayed in the time domain. The Fourier Transform (or Fourier analysis) is a way to switch into the frequency domain. The Inverse Fourier Transform (or Fourier synthesis) is a way to go back again to the time domain. The Fourier Transform is converting a continuous signal, a function of time x(t) to a continuous signal, a function of frequency X(f).
How will this be done? Fourier (among others) proved that any continuous signal can be represented as a sum of sinusoids. Now, I could present a fancy formula here, and I will, but let's first think about it a bit. What helped me most in understanding the Fourier Transform is this; what if we want to see how much of anything is contained in anything else in math? Right, we divide; to see...