Local sound field reproduction using digital signal processing

This work shows how an acoustic wavefront can be reconstructed locally by using only a few loudspeakers. The loudspeaker inputs are calculated by passing a set of signals recorded by only a few microphones through a matrix of causal digital filters having finite impulse responses. These filters, referred to as the inverse filters, are calculated by inverting (in the least-squares sense) a matrix which contains the electroacoustic transfer functions from the loudspeakers to the microphones. In practice, it is crucial to use a modeling delay and a regularization factor in order to achieve an accurate inversion. The technique is illustrated with an example that shows how well four loudspeakers can reproduce a sound field that has been recorded with three microphones. When the recorded field does not contain energy at frequencies whose acoustical wavelengths are shorter than the distance between adjacent microphones, the original field is reproduced remarkably accurately in the vicinity of the microphones regardless of the positions of the loudspeakers.