Analytical Approach to Wave Field Reconstruction Filtering in Spatio-Temporal Frequency Domain

For transmission of a physical sound field in a large area, it is necessary to transform received signals of a microphone array into driving signals of a loudspeaker array to reproduce the sound field. We propose a method for transforming these signals by using planar or linear arrays of microphones and loudspeakers. A continuous transform equation is analytically derived based on the physical equation of wave propagation in the spatio-temporal frequency domain. By introducing spatial sampling, the uniquely determined transform filter, called a wave field reconstruction filter (WFR filter), is derived. Numerical simulations show that the WFR filter can achieve the same performance as that obtained using the conventional least squares (LS) method. However, since the proposed WFR filter is represented as a spatial convolution, it has many advantages in filter design, filter size, computational cost, and filter stability over the transform filter designed by the LS method.