  Discoveries of RR Lyrae and Cepheid variable stars with multiple modes of
pulsation have increased tremendously in recent years. The Fourier spectra of
these stars can be quite complicated due to the large number of combination
frequencies that can exist between their modes. As a result, light-curve fits
to these stars often suffer from undesirable ringing effects that arise from
noisy observations and poor phase coverage. These non-physical overfitting
artifacts also occur when fitting the harmonics of single-mode stars as well.
Here we present a new method for fitting light curves that is much more robust
against these effects. We prove that the amplitude measurement problem is very
difficult (NP-hard) and provide a heuristic algorithm for solving it quickly
and accurately.
