  Inspiral signals from binary black holes, in particular those with masses in
the range $10M_\odot \lsim M \lsim 1000 M_\odot,$ may last for only a few
cycles within a detector's most sensitive frequency band. The spectrum of a
square-windowed time-domain signal could contain unwanted power that can cause
problems in gravitational wave data analysis, particularly when the waveforms
are of short duration. There may be leakage of power into frequency bins where
no such power is expected, causing an excess of false alarms. We present a
method of tapering the time-domain waveforms that significantly reduces
unwanted leakage of power, leading to a spectrum that agrees very well with
that of a long duration signal. Our tapered window also decreases the false
alarms caused by instrumental and environmental transients that are picked up
by templates with spurious signal power. The suppression of background is an
important goal in noise-dominated searches and can lead to an improvement in
the detection efficiency of the search algorithms.
