The Plenacoustic Function and its Sampling

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. We observe that the multidimensional spectrum of the solution of the wave equation has an almost bandlimited character. Therefore sampling and interpolation can easily be applied using signals on an array. The decay of the spectrum is studied on both temporal and spatial frequency axes. We study how this decay influences the performance of the interpolation. Based on the support of the spectrum, we determine the number and the spacing between the microphones needed to reconstruct the sound field up to a certain temporal frequency. The optimal sampling pattern for the microphone positions is given for the linear and the planar case. 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 the sound field in a finite number of positions and with this information the total sound field can be recreated. Finally, simulations and experimental results are presented and compared with the theory.