[codebaobab]

I heard once that the circles-on-circles construction of the motion of the bodies of solar system when Earth is taken as its center is merely the Fourier transform of the ellipses that describe the solar system with the Sun as its center.

Unfortunately, I never saw the actual derivation, so that idea is basically hearsay.

[Locke1689]

I think you misheard. The epicycle system is, in essence, an n-termed complex Fourier series (not transform). The point that the person who told you this was trying to make was that any path can be represented using enough terms in a complex Fourier series, so it's a fairly bad system for deriving physical laws.