  The Crab Pulsar's radio emission is unusual, consisting predominantly of
giant pulses, with durations of about a micro-second but structure down to the
nano-second level, and brightness temperatures of up to $10^{37}\,$K. It is
unclear how giant pulses are produced, but they likely originate near the
pulsar's light cylinder, where corotating plasma approaches the speed of light.
We report observations in the 400-800 MHz frequency band, where the pulses are
broadened by scattering in the surrounding Crab nebula. We find that some pulse
frequency spectra show strong bands, which vary during the scattering tail, in
one case showing a smooth upward drift. While the banding may simply reflect
interference between nano-second scale pulse components, the variation is
surprising, as in the scattering tail the only difference is that the source is
observed via slightly longer paths, bent by about an arcsecond in the nebula.
The corresponding small change in viewing angle could nevertheless reproduce
the observed drift by a change in Doppler shift, if the plasma that emitted the
giant pulses moved highly relativistically, with a Lorentz factor
$\gamma\sim10^4$ (and without much spread in $\gamma$). If so, this would
support models that appeal to highly relativistic plasma to transform ambient
magnetic structures to coherent GHz radio emission, be it for giant pulses or
for potentially related sources, such as fast radio bursts.
