  Due to the importance of accurate Fourier parameters, we devise a method that
is more appropriate for deriving these parameters on low-quality data than the
traditional Fourier fitting. Based on the accurate light curves of 248
fundamental mode RR Lyrae stars, we test the power of a full-fetched
implementation of the template method in the computation of the Fourier
decomposition. The applicability of the method is demonstrated also on datasets
of filter passbands different from that of the template set. We examine in more
detail the question of the estimation of Fourier- based iron abundance [Fe/H]
and average brightness. We get, for example, for light curves sampled randomly
in 30 data points with sigma=0.03 mag observational noise that optimized direct
Fourier fits yield sigma_[Fe/H]=0.33, whereas the template fits result in
sigma_[Fe/H]=0.18. Tests made on the RR Lyrae database of the Large Magellanic
Cloud (LMC) of the Optical Gravitational Lensing Experiment (OGLE) support the
applicability of the method on real photometric time series. These tests also
show that the dominant part of error in estimating the average brightness comes
from other sources, most probably from crowding effects, even for under-sampled
light curves.
