Fourier inversion theorem

The Fourier Inversion Theorem is like a mathematical trick that helps us understand how to break down a complicated signal (like a sound wave) into its simple pieces. It works like this: let's say you have a really loud signal, like the sound of an airplane engine. We can use the Fourier Inversion Theorem to split the signal into a bunch of simpler pieces. Each of those pieces is like one of the notes the airplane engine makes. So instead of one loud signal, now we have a bunch of simpler notes, and they're all much easier to understand.