Interpolation of device-related transfer functions of microphone arrays

With the growing applications of spatial audio, it is desirable to capture three-dimensional content using microphones embedded in devices of various structures without relying on regular array geometries. This requires the accurate measurement and modeling of the acoustic transfer function of each microphone as a function of the arrival direction, capturing the scattering and diffraction from the device's body. This is commonly known as device-related transfer function (DRTF) and can be measured in an anechoic room over a finite number of directions. In this work, we propose a theoretical framework to interpolate the DRTF to any direction using reproducing-kernel Hilbert spaces (RKHS) on the 3-D sphere. Specifically, we use the von Mises–Fisher kernel, which naturally fits directional data. As an illustration, we use a microphone embedded in a rigid sphere as a simulation example to validate the theoretical derivations.