Least squares approach in wavenumber domain for sound field recording and reproduction using multiple parallel linear arrays

A novel signal processing method is proposed for sound field recording and reproduction using multiple parallel linear microphone and loudspeaker arrays. In sound field recording and reproduction, the problem is how to calculate the transfer filters that transform the signals recorded by microphones into the driving signals of the loudspeakers. The proposed method is based on the spatial Fourier transform in the horizontal angle combined with the least squares (LS) approach in the elevation angle. In the proposed method, the signals recorded by each linear microphone array and those that drive each loudspeaker array are decomposed into the wavenumber domain by the spatial Fourier transform in the horizontal direction. The transfer filters are then calculated by the LS approach in the wavenumber domain. As a result, the size of the matrix of each transfer function in the wavenumber domain is much smaller than that of the conventional LS approach in the temporal frequency domain (LSTF), and well-conditioned stable transfer filters can be obtained with low computational cost without regularization. Computer simulation results show that the proposed method reconstructed a sound field around the control points as accurately as the conventional LSTF.