  We report a method to determine the phase and amplitude of sinusoidally
modulated event rates, binned into four bins per oscillation, based on data
generated at the resonant neutron spin-echo spectrometer RESEDA. The presented
algorithm relies on a reconstruction of the unknown parameters. It omits a
calculation intensive fitting procedure and avoids contrast reduction due to
averaging effects. It allows the current data acquisition bottleneck at RESEDA
to be relaxed by a factor of four and thus increases the potential time
resolution of the detector by the same factor. We explain the approach in
detail and compare it to the established fitting procedures of time series
having four and 16 time bins per oscillation. In addition we present the
empirical estimates of the errors of the three methods and compare them to each
other. We show that the reconstruction is unbiased, asymptotic, and efficient
for estimating the phase. Reconstructing the contrast increases the error bars
by roughly 10% as compared to fitting 16 time binned oscillations. Finally, we
give heuristic, analytical equations to estimate the error for phase and
contrast as a function of their initial values and counting statistics.
