Close-talking spherical microphone array using sound pressure interpolation based on spherical harmonic expansion

We propose a novel close-talking spherical microphone array that uses the residual signal between the observed sound pressure and the interpolated sound pressure at the center of the spherical array. The interpolated sound is obtained from the sound pressures observed on the surface of a sphere on the basis of the spherical harmonic expansion, assuming that the sound originates from the outside of the array. If the sound source is close to the spherical array, the array cannot express the spherical wave correctly because the number of microphones is limited. As a result, the residual signal increases. This method is a modified form of the conventional method, which interpolates the sound pressure by using the Kirchhoff integral equation. In contrast with the conventional method, we interpolate the sound at the center of the sphere by using only the average value of the sound pressures on the spherical array surface. The computer simulations were conducted using a 12-element spherical microphone array with radius of 5 cm. These results showed that the performances of both methods were almost equivalent, although the proposed method used half the number of microphones as the conventional method.