Angular and Radial Directivity Control for Spherical Loudspeaker Arrays

Diploma Thesis (pdf 3.614KB)

Spherical loudspeaker arrays, as concerned within this work, are a finite set of transducers distributed on the surface of a sphere or platonic solid. The purpose of these arrays is to synthesize artificial acoustic radiation or to reproduce natural sound sources. This relatively recent research topic is applicable in many fields, such as musical performances or acoustic measurements. The present thesis develops and discusses a control system for directivity pattern synthesis using an icosahedral loudspeaker array. In order to obtain sensible control parameters a surrounding spherical microphone array is used to measure the individual directivities of the array transducers. Basically, weighted combinations already create variable directivity directly at the measurement radius. It is, however, advantageous to decompose these directivities into orthogonal spherical harmonic components. At this radius the spherical harmonics provide directivity synthesis with well defined angular resolution and simple relations for rotation of synthesis patterns. Arbitrarily, synthesis patterns will appear blurred at other radii due to sound propagation. Inherently, the spherical harmonics are only affected by well-defined gain and phase changes but retain their individual shape. Efficient time-domain radial steering filters are introduced to focus the synthesis pattern to specific radii. The limitations of the over-all control systems are being investigated.