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 extraterrestrial civilizations. We estimate scintillation parameters for extragalactic sources that take into account scattering both in the host galaxy and in foreground Galactic plasma.
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