Acoustics 08 Paris
7331With an appropriate control system, directivity pattern synthesis can be accomplished with spherical loudspeaker arrays, e.g. in the shape of Platonic solids or spheres. The application of such devices for the reproduction of natural or artificial directivity patterns poses a relatively young field of research in computer music and acoustic measurements. Using directivity measurements with microphones, the directivity patterns of the individual speakers on the array can be determined. Usually, the directivity of the whole array may be regarded as a linear combination of these patterns. In order to gain control, the measurement data of the linear system need to be inverted. Given L loudspeakers and M microphones, this inversion yields the desired control system, an expensive LxM multiple-input-multiple-output (MIMO) filter. We introduce discrete spherical harmonics transform and decoder matrices to reduce the number of channels required for this control system, thus reducing the computational effort. However, this step often leads to a sparse MIMO-system, in which many off-diagonal transfer functions vanish. If applicable, the computation of the non-zero transfer functions only can be done at even much lower cost. A case study for an icosahedral loudspeaker array is given, showing the properties of the sparse MIMO-system.
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