Three-dimensional panning by four loudspeakers and its solution

This paper proposes a 3D panning method based on particle velocity and sound pressure by four loudspeakers for synthesizing a virtual sound source. Firstly, according to the requirements of maintaining sound physical properties strictly, the distribution coefficients of four loudspeakers are calculated by the coordinates of four loudspeakers and a virtual sound source. If the distribution coefficients is not all positive, we maintain the direction of particle velocity and sound pressure to get a series of feasible solutions. Then optimal distribution coefficients of four loudspeakers are chosen through minimizing the error of particle velocity from these feasible solutions. Objective experiment demonstrates that this method can make mean error of sound pressure at most about 19.3% lower than Ando's method around spherical center in equatorial plane. Subjective experiment shows that the proposed method performs better than Ando's method.