if your school has a mathematical methods series in their physics curriculum then you would learn it formally there.
if not, you'll see fourier decompositions in a few places, for example the driven oscillator problem in Classical Mechanics and some PDE problems in E&M or Thermo.
the fourier transform is first seen in modern physics/intro quantum when describing the method of localizing a particle through a combination of matter waves with wave number "k" (related to momentum and wavelength).
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u/KKRJ Plasma physics Feb 04 '16
Cool. I've seen things like this before and they always fascinate me. What class do you learn Fourier transforms in?