  When a source emits a gravity-wave (GW) pulse over a short period of time,
the leading edge of the GW signal is redshifted more than the inner boundary of
the pulse. The GW pulse is distorted by the gravitational effect of the
self-energy residing in between these shells. We illustrate this distortion for
GW pulses from the final plunge of black hole (BH) binaries, leading to the
evolution of the GW profile as a function of the radial distance from the
source. The distortion depends on the total GW energy released and the duration
of the emission, scaled by the total binary mass, M. The effect should be
relevant in finite box simulations where the waveforms are extracted within a
radius of <~ 100M. For characteristic emission parameters at the final plunge
between binary BHs of arbitrary spins, this effect could distort the simulated
GW templates for LIGO and LISA by a fraction of 0.001. Accounting for the wave
distortion would significantly decrease the waveform extraction errors in
numerical simulations.
