- A new time domain (TD) representation for radiation from apertures, wherein the field is expanded in a discrete lattice of shifted, tilted, and retarded pulsed beam (PB) propagators is proposed. The PB representation provides a uniformly accurate systematic framework for ray-based tracking of ultrawide-band transient fields in complex configurations, e.g., slowly or abruptly varying inhomogeneous media. The excitation coefficients of the PBs are extracted from the aperture source distribution via a new "discretized local slant stack transform". The formulation is structured upon a new class of frames, termed windowed Radon transform frames. The sets of expansion and analysis functions are shown to be dual frames, thus, facilitating representation of arbitrary bandlimited source fields. Explicit expressions for the processing windows (the analysis frame set) and for the PB propagators (the expansion set) are provided for the class of isodiffracting PBs. Accuracy of the PB expansion technique is demonstrated for a focusing aperture case, that tends to fail the conventional ray shooting schemes.