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Description
Parametric representations of wavefields are central to sound field estimation and reconstruction, where capturing both propagation geometry and localization is essential. We introduce a parametric framework, called Gaussian boostlet kernels, a variation of boostlets that uses Gaussian functions to control their frequency bandwidth and phase-speed selectivity (geometric spread). We explore the expressive power of these boostlet kernels through asymptotic limits in which the Gaussian widths become infinitely broad or narrow. This analysis reveals four distinct regimes. When both frequency bandwidth and geometric spread vanish, the kernel reduces to a classical monochromatic plane wave. Vanishing frequency bandwidth and broad geometric spread yield cylindrical wavefields represented by Hankel functions, capturing a boosted superposition of plane waves. Conversely, infinite frequency bandwidth and vanishing geometric spread produce transient plane-wave sources localized along characteristic rays, consistent with trace-wave interpretations in array acoustics. In the fully broadband limit, the kernel converges to the space–time Dirac delta, equivalent to the Green’s function source. These findings demonstrate that Gaussian boostlet kernels smoothly interpolate between plane and cylindrical eigenfunctions, and between impulsive plane and point sources. This provides a geometric connection among wavenumber processing, Green’s function formulations, and wavefield decompositions, and shows potential for parametric sound-field reconstruction, source separation, and room-acoustics analysis.