Several approaches are presented to compute the acoustic transient field from planar axisymmetric circular sources vibrating with continuous space/time velocity distributions. These approaches include an impulse response approach for uniformly vibrating sources, and a generalized impulse response approach and a source discretization approach for nonuniformly vibrating sources. Also, two approximations for the far field will be overviewed. As a particular case of interest and importance, the acoustic field generated by a space/time modified power spectrum (MPS) driving pulse will be described using the various approaches. Numerical results are presented to illustrate the localized behavior of the space/time field. These results are compared to analogous results obtained from ordinary cw driving pulses. Methods to optimize the localization power of the MPS pulse are also discussed.