  The Burst Alert Telescope (BAT) on board Swift has accumulated extensive
light curves for 265 sources (not including GRBs) in the energy range 14 to 200
keV. We present here a summary of searches for periodic modulation in the flux
from X-ray binaries. Our results include: determination of the orbital periods
of IGR J16418-4532 and IGR J16320-4751; the disappearance of a previously known
9.6 day period in 4U 2206+54; the detection of a 5 hour period in the symbiotic
X-ray binary 4U 1954+31, which might be the slowest neutron star rotation
period yet discovered; and the detection of flares in the supergiant system 1E
1145.1-6141 which occur at both periastron and apastron passage with nearly
equal amplitude. We compare techniques of weighting data points in power
spectra and present a method related to the semi-weighted mean which, unlike
conventional weighting, works well over a wide range of source brightness.
