Digital acoustics: processing wave fields in space and time using DSP tools

Systems with hundreds of microphones for acoustic field acquisition, or hundreds of loudspeakers for rendering, have been proposed and built. To analyze, design, and apply such systems requires a framework that allows us to leverage the vast set of tools available in digital signal processing in order to achieve intuitive and efficient algorithms. We thus propose a discrete space–time framework, grounded in classical acoustics, which addresses the discrete nature of the spatial and temporal sampling. In particular, a short-space/time Fourier transform is introduced, which is the natural extension of the localized or short-time Fourier transform. Processing in this intuitive domain allows us to easily devise algorithms for beam-forming, source separation, and multi-channel compression, among other useful tasks. The essential space band-limitedness of the Fourier spectrum is also used to solve the spatial equalization task required for sound field rendering in a region of interest. Examples of applications are shown.