Frame-Based Beam-Summation Algorithms for Ultra Wideband Radiation from Extended Apertures. Part II: Time domain formulation

The wideband frame-based beam summation algorithms introduced in the first part of this two parts sequence1 (see also Ref. 2) have several attractive features that make them amenable for an extension into the Time Domain (TD): (a) The same beam lattice is used for all frequencies; (b) The iso-diffracting Gaussian beam (IDGB) basis provides the ``snuggest'' frame representation for all frequencies; (c) The propagation parameters of the resulting beams are frequency-independent and need to be calculated only once at a reference frequency. These properties were utilized in Ref. 3 to derive new TD representations for radiation from extended apertures, wherein the field is expanded in a discrete phase space lattice of shifted and tilted iso-diffracting pulsed beam propagators (ID-PB). The excitation coefficients of these propagators are extracted from the aperture source distribution by using the ID-PBs as ``analysis windows'' in a ``discrete local slant stack transform'' (DL-SST). From a broader perspective, this transform involves a new class of Radon-frames and can be regarded as a ``discrete local Radon transform'' in ℝ3 that may be relevant in other disciplines, such as image processing.