3-D SOUND SOURCE RECONSTRUCTION AND FIELD REPREDICTION USING THE HELMHOLTZ INTEGRAL-EQUATION

A method for reconstruction of the boundary conditions of an arbitrarily shaped three-dimensional (3-D) sound source from a finite number of field pressures is presented and the associated field is repredicted by using the Helmholtz integral equation. To minimize the reconstruction error due to noise in the field pressures, a filtering method is proposed and it is verified that numerically singular values which correspond to the higher-order modes of the evanescent-like components of the source velocities are eliminated. For arbitrarily shaped sources with complex boundary conditions, the reconstruction is performed accurately when the size of each element is less than a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of a sphere in the vicinity of the source. Our technique can be used in computer-aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from the finite number of field pressures and repredicts the variation of the sound field procuced by a redesigned loudspeaker cabinet on which the reconstructed diaphragm is mounted. © 1990.