  Coupled nonlinear systems under certain conditions exhibit phase
synchronization, which may change for different frequency bands or with
presence of additive system noise. In both cases, Fourier filtering is
traditionally used to preprocess data. We investigate to what extent the phase
synchronization of two coupled R\"{o}ssler oscillators depends on (1) the
broadness of their power spectrum, (2) the width of the band-pass filter, and
(3) the level of added noise. We find that for identical coupling strengths,
oscillators with broader power spectra exhibit weaker synchronization. Further,
we find that within a broad band width range, band-pass filtering reduces the
effect of noise but can lead to a spurious increase in the degree of
synchronization with narrowing band width, even when the coupling between the
two oscillators remains the same.
