  We discuss optimal detection of fast radio transients from astrophysical
objects while taking into account the effects of propagation through
intervening ionized media, including dispersion, scattering and
scintillation.Our analysis applies to the giant-pulse phenomenon exhibited by
some pulsars, for which we show examples, and to radio pulses from other
astrophysical sources, such as prompt radio emission from gamma-ray burst
sources and modulated signals from extra-terrestrial civilizations.
