  The measurement of electron cloud densities in particle accelerators using
microwaves has proven to be an effective, non-invasive and inexpensive method.
So far the experimental schemes have used continuous waves. This has either
been in the form of travelling waves that are propagated, or standing waves
that are trapped, in both cases within a segment of the accelerator chamber.
The variation in the wave dispersion relation caused by the periodic creation
and decay of the electron cloud leads to a phase modulation in the former case,
and a frequency modulation in the latter. In general, these methods enable the
measurement of a time averaged electron cloud density. In this paper we propose
a time resolved measurement by using pulses propagated over a finite length of
the accelerator chamber. The pulses are launched periodically, once after a
bunch train has passed and then again half a revolution period later. This
results in pulses alternating between a dispersion that is either affected by a
cloud or not. The resulting spectrum of the signal can be related to the
electron density sampled by the pulse that propagates through the cloud. By
varying the delay of the launch of the pulse with respect to the train passage,
one can map the cloud density at different points behind the train.
