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Coping with complex wave phenomena, especially at high frequencies, requires detailed understanding of the spectral as well as the configurational behavior of the fundamental wave constituents employed in field synthesis. These aspects can be treated in a phase space that covers simultaneously the configurational and spatial wave number variables for the time harmonic regime, with the addition of time and frequency variables for the transient regime. Although it represents the most general format, the full phase space constructed in this manner may not be the most convenient for tracking physical observables. Better suited may be reduced or partial phase space representations based on the spectral decomposition of only some of the space-time variables. Various choices in the reduction lead to alternative representations with different physical content, and to corresponding alternative parametrizations of the radiation and propagation process. As part of a general study in both the frequency and time domains, the present paper concentrates on time harmonic spatial and spectral representations that contain sampling windows. Such sampling, either discrete or continuous, formalizes the localization that plays an important role in high frequency wave phenomena. The analytical machinery, together with asymptotic constructs that provide physical interpretation in terms of beams, is developed here for radiation from plane aperture sources.