  The detection of pulsations from an X-ray binary is an unambiguous signature
of the presence of a neutron star in the system. When the pulsations are missed
in the radio band, their detection at other wavelengths, like X-ray or
gamma-rays, requires orbital demodulation, since the length of the observations
are often comparable to, or longer than the system orbital period. The detailed
knowledge of the orbital parameters of binary systems plays a crucial role in
the detection of the spin period of pulsars, since any uncertainty in their
determination translates into a loss in the coherence of the signal during the
demodulation process. In this paper, we present an analytical study aimed at
unveiling how the uncertainties in the orbital parameters might impact on
periodicity searches. We find a correlation between the power of the signal in
the demodulated arrival time series and the uncertainty in each of the orbital
parameters. This correlation is also a function of the pulsar frequency. We
test our analytical results with numerical simulations, finding good agreement
between them. Finally, we apply our study to the cases of LS 5039 and LS I +61
303 and consider the current level of uncertainties in the orbital parameters
of these systems and their impact on a possible detection of a hosted pulsar.
We also discuss the possible appearance of a sideband ambiguity in real data.
The latter can occur when, due to the use of uncertain orbital parameters, the
power of a putative pulsar is distributed in frequencies lying nearby the
pulsar period. Even if the appearance of a sideband is already a signature of a
pulsar component, it may introduce an ambiguity in the determination of its
period. We present here a method to solve the sideband issue.
