In the design of sound reproduction systems for semi-reverberant rooms, time-domain solutions allow the use of methods which can shape the net responses which is useful for reducing perceptual artefacts. In this paper the time domain functions associated with the radial functions of 2D and 3D point sources are derived. These functions consist of the product of a Bessel and a Hankel function. The time-domain functions provide insight into how the sound field is produced. The solutions are used to develop a mode-based, time-domain approach to sound field reproduction. Comparisons are made with a frequency-domain solution.
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