Regularized Spherical Fourier Transform for Room Impulse Response Interpolation

Room impulse responses (RIRs) are a key tool in architectural acoustics and spatial sound for virtual reality. They characterize the room response between a sound source and a receiver. Directional RIRs at the receiver position can be measured with spherical microphone arrays or calculated with 3D models and numerical methods. Either because of a low number of microphones or limited computational capacity, there is a need to interpolate the RIRs to obtain higher directional resolutions. The spherical Fourier transform (SFT) enables a promising physics-based interpolation approach. However, existing SFT algorithms for acoustic purposes highly depend on the spherical distribution of microphones. This paper presents a SFT algorithm based on Tikhonov regularization that is suitable for random spherical distributions. Results show that the regularized SFT maintains the interpolation error bounded at high-energy values in time and up to a maximum frequency determined by the number of microphones. An open-source implementation is made publicly available to foster the reproducibility of this research.