A review of some analytic techniques and wave solutions that are relevant to the analysis of ultra wideband short-pulse fields and data is presented. A simple problem of short-pulse radiation from an aperture distribution is considered. Ultra wideband excitations in the short-pulse case are handled by formulating the radiation integral directly in the time domain. Studies of characteristics of a pulsed beam (PB) show that the axial confinement along the beam axis is due to the pulsed behavior while transverse confinement is due to analytic signals. Studies of complex source pulsed beams (CSPB) show that they are globally exact wave-packet solutions of the time-dependent wave equation that can be modeled mathematically in terms of radiation from a pulsed source located at a complex coordinate point. It is also found that all frequency components in the PB are Gaussian beams with the same waist planes and collimation distances.