The Fourier Transform breaks down a function (e.g., over time) into components that are periodic functions. The forward transformation is:
F(s) is ∞ ∫ f(x)e-2πisxdx -∞
There is also an inverse transform, from s to x.
The Fourier transform is used to determine what sine-like components make up a particular periodic function, i.e., break a signal down into its harmonics.
Canada-France-Hawaii Telescope (CFHT)
Fast Fourier Transform (FFT)
Imaging Fourier Transform Spectroscopy (IFTS)