The problem of reconstruction of the moments of a function from its central projections is discussed when the range of one of the variables is limited. The theory is then considered in the context of incoherent scatter radar observation of the ionosphere with a chirped radar system. The combination of the chirp technique with special phase coding schemes is also considered but is found unattractive in most cases because of the strict requirements on time stationarity of the medium, a situation which often does not exist.¿ 1997 American Geophysical Union