Modal reconstruction of the sound field in a room at low frequencies

Capturing the spatio-temporal (or spatio-spectral) properties of the sound field in a room is valuable for its characterization. To measure the full spatio-spectral properties within the volume of the room, i.e., the frequency response functions at all points, a very large number of measurements is required. Even at low frequencies, sampling the three-dimensional space enclosed by a room is challenging. It is therefore of interest to employ sound field reconstruction methods to predict (interpolate/extrapolate) the sound field over the volume of the room, based on a limited number of measurements. The aim of this study is to develop a sound field reconstruction method that exploits the modal structure of the sound field in a room, to reconstruct the sound field at low frequencies over the entire volume of the space. The proposed methodology makes use of the fact that the spatial structure of the acoustic field in a room is inherently block-sparse and can be extracted from spatially distributed measurements. The modeshapes are represented as the superposition of a small number of plane waves, and the modal basis is used to reconstruct the sound field.