Radiation Lobe Decomposition for Directivity Patterns

Paper in proceeding, 2021

We propose a decomposition of sound source directivity patterns expressed by spherical harmonics coefficients into a set of radiation lobes. The method reveals the direction, magnitude and two-dimensional curvature at the peak of the radiation lobes, and facilitates novel ways for the resynthesis of modified directivities. We define Newton’s method on the surface of the sphere via recurrence relations of the spherical harmonics to find the direction and amplitude of the radiation lobes. The curvatures at the peaks of the lobes are determined via the Hessian. We use the parametric description of the radiation lobes to resynthesize simplified minimum-norm directivities by neglecting low-magnitude radiation lobes and by reducing the spherical harmonics reproduction order. The decomposition approach can reveal valuable information about the directivity of musical instruments and facilitates practical trade-offs in storage and rendering of directivity patterns.