  Cyclic spectroscopy is a signal processing technique that was originally
developed for engineering applications and has recently been introduced into
the field of pulsar astronomy. It is a powerful technique with many attractive
features, not least of which is the explicit rendering of information about the
relative phases in any filtering imposed on the signal, thus making holography
a more straightforward proposition. Here we present methods for determining
optimum estimates of both the filter itself and the statistics of the
unfiltered signal, starting from a measured cyclic spectrum. In the context of
radio pulsars these quantities tell us the impulse response of the interstellar
medium and the intrinsic pulse profile. We demonstrate our techniques by
application to 428 MHz Arecibo data on the millisecond pulsar B1937+21,
obtaining the pulse profile free from the effects of interstellar scattering.
As expected, the intrinsic profile exhibits main- and inter-pulse components
that are narrower than they appear in the scattered profile; it also manifests
some weak, but sharp features that are revealed for the first time at low
frequency. We determine the structure of the received electric-field envelope
as a function of delay and Doppler-shift. Our delay-Doppler image has a high
dynamic-range and displays some pronounced, low-level power concentrations at
large delays. These concentrations imply strong clumpiness in the ionized
interstellar medium, on AU size-scales, which must adversely affect the timing
of B1937+21.
