A diffusion device based on a digitally-controlled 3D array of loudspeakers was developed in order to synthesize a given radiation pattern from the combination of a set of elementary directivities. This radiation synthesis method, designed for musical and performance purposes (real-time control, musical vocabulary associated to different directivity patterns, …), has been used in concerts and sound installations. In order to transpose the sound experience from stage to domestic contexts, the paper addresses the post-production step where the spatial sound image associated to the radiation synthesis has to be trans-coded for conventional playback setup like stereo or 5.1. The method is based on the acoustical characterization of the performance situation with the different elementary directivities which are then combined according to the musical score.