Great, the Hill differential equations are good star to study periodic functions a coefficients. You could replace the Fourier expansion by Wavelet equations which minimize an error function. I had given your a sample which could download in MML.
So f(t) in Hill equation could be the SVR regressor! in wavelet form so it gives you two things a) local periodicity b) minimzing some error function.
I actually like to experiment and code some of your ideas with this Hill thingy you found