The Plenacoustic Function and Its Sampling

TLDR

The spatialization of sound fields in rooms, including the evolution of room impulse responses with position, is typically modeled using room models, but this study focuses on the direct measurement of sound pressure fields across space. The study aims to develop a method that reconstructs the sound pressure field at arbitrary spatial positions from measurements at a finite set of points. The authors use array-based sampling and interpolation of the wave equation’s almost bandlimited spectrum, analyzing its temporal and spatial decay to determine microphone number, spacing, and optimal patterns for linear, planar, and 3D reconstruction up to a target frequency. They find that the wave equation’s spectrum is nearly bandlimited, that its decay affects interpolation accuracy, and that the derived optimal microphone patterns yield accurate reconstructions confirmed by simulations and experiments.

Abstract

The spatialization of the sound field in a room is studied, in particular the evolution of room impulse responses as a function of their spatial positions. It was observed 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. The influence of the decay on the performance of the interpolation is analyzed. Based on the support of the spectrum, the number and the spacing between the microphones is determined for the reconstruction of the sound pressure field up to a certain temporal frequency and with a certain reconstruction quality. The optimal sampling pattern for the microphone positions is given for the linear, planar and three-dimensional case. Existing techniques usually make use of room models to recreate the sound field present at some point in the space. The presented technique simply starts from the measurements of the sound pressure field in a finite number of positions and with this information the sound pressure field can be recreated at any spatial position. Finally, simulations and experimental results are presented and compared with the theory