Spherical t-Design for Characterizing the Spatial Response of Microphone Arrays

Microphone arrays are usually employed for spatial audio recordings and analysis. This requires converting the raw signals of the capsules into a 3D audio format, e.g., a spherical harmonics expansion. For processing such conversion, namely beamforming, it is necessary to know the complex response of each microphone of the array for many Directions-of-Arrival of the sound waves. This information constitutes the spatial response and describes how the wave fronts are diffracted by the surface of the array. Beyond the experimental, numerical, or theoretical method employed to get the spatial response, the shape of the array and the number of capsules, the choice of the Directions-of-Arrival of the sound waves is always critical. On one side, to maximize the spatial information and so the performance, on the other side to reduce the number of directions, and so the measurement or calculation time. The paper analyzes the problem of choosing an optimal geometry for obtaining the spatial response of a microphone array. It will be shown that spherical design, or T-design, allows maximizing the spatial information with the minimum amount of testing directions. Numerical and theoretical methods have been employed for characterizing two microphone arrays, a spherical and a non-spherical one. In both cases, Ambisonics format for spatial audio has been employed.