Spatio-temporal Properties of Simulated Impulse Responses on a Rigid Sphere
Rigid spherical microphone arrays are widely used for sound field analysis due to its compact size, uniform spatial resolution and numerical stability. Simulating the microphone signals is a useful tool to evaluate analysis techniques in different scenarios. The simulations are typically performed in the frequency domain by exploiting the analytic expression of the spatial transfer functions which is described in terms of the derivative of the spherical Hankel functions. Despite its accuracy in the frequency domain, the simulation is computationally demanding and the resulting impulse responses exhibit pre-echos and temporal aliasing. In this paper, an alternative approach is presented where the spatial impulse responses are modeled as infinite impulse response (IIR) filters. It not only enables a more efficient simulation but also avoids the above-mentioned temporal artifacts. The polynomial expressions of the spherical Hankel functions are converted either into factorized second-order sections or partial fraction expansions. A digital filter corresponding to each harmonic order is built by mapping the parameters from the Laplace domain to the z domain. The spatio-temporal structure of the simulated impulse responses are examined, where the influence of different mapping methods (bilinear transform, matched-z transform, and the corrected impulse invariant method) are investigated.