We describe two methods, suitable for routine application to teleseismic recordings, that characterize the time history of seismic events. Stacking short-period signals from large regional arrays provides stable estimates of high-frequency radiation from the source, and an empirical Green's function deconvolution procedure extracts reliable, broadband time functions suitable for analysis of faulting complexity and the spatio-temporal extent of rupture. Combined, these procedures characterize the source radiation of large events (Ms > 7) between 200- and 0.5-sec periods.