where there are two planets orbiting the same star, and the orbital period ratio of the two planets is not in a ratio of small integers (i.e., the non-resonant orbits in a scientific jargon). There is a well known mathematical method, known as the Lie-Hori perturbation theory, that can be applied to this case. Furthermore, in practice, the observational coverage of any given system is relatively short, years to tens of years max. So, one only needs to consider the short-period variations, and ignore everything else. This turns out to be relatively easy. The interaction potential is expanded in the Fourier series and the short-period variations of orbital elements emerge in the Lie-Hori theory as derivatives of the generating function, which is closely related to the original Fourier expansion. The variations are then plugged into an expression for TTVs, and voila, the TTVs are given as the Fourier series as well.

I reasoned that an observer can take the TTV data and perform the Fourier analysis, thus identifying frequencies, amplitudes, and phases of whatever terms the measurements contain. The short-period frequencies must be $k_1 n_1 + k_2 n_2$, where $k_1$ and $k_2$ are small integers, and $n_1$ and $n_2$ the 