The plenacoustic function, sampling and reconstruction

We study the spatialization of the sound field in a room, in particular the evolution of room impulse responses as a function of their spatial positions. The presented technique allows us to characterize completely the sound field in any arbitrary location if the sound field is known in a certain finite number of positions. Existing techniques usually make use of room models to recreate the sound field present at some point in the space. Our technique simply starts from the measurements of impulse responses at a finite number of positions, and, with this information, the total sound field can be recreated. An analytical solution of the problem is given for different cases of spaces. Further, we determine the number of microphones and the spacing between them needed to reconstruct the sound field perfectly up to a certain temporal frequency. The optimal sampling pattern for the microphone positions is given. Applications are also discussed.