  We report a method to determine the phase and amplitude of sinusoidally
modulated event rates, binned into 4 bins per oscillation. 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 to be
relaxed by a factor of 4. Here, we explain the approach in detail and compare
it to the established fitting procedures of time series having 4 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, which corresponds to the amplitude of the
modulation, is roughly 10% less efficient than fitting 16 time binned
oscillations. Finally, we give analytical equations to estimate the error for
phase and contrast as a function of their initial values and counting
statistics.
