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Acoustic boundary value problems and their application to partial spherical microphone arrays

Authors Pomberger, H.
Year 2017
Thesis Type Doctoral thesis
Topic Spatial Audio
Keywords audio recording and reproduction, signal processing, Ambisonics
Abstract This thesis develops a general concept for microphone arrays located on a partial spherical surface, which is enclosed by rigid angular boundaries. These partial spherical arrays inherently capture only sound sources from directions within the rigid boundaries. Thus they are especially suitable for scenarios where only sources within this directional range are of interest. The theoretical foundation of partial spherical microphone arrays is the solution of the Helmholtz equation in spherical coordinates, with boundary conditions in azimuth and zenith angle. The angular solutions form a complete set of orthonormal functions on the partial spherical surface. These allow for a modal decomposition of the sound field within the lim- ited directional range, similar to the spherical harmonics decomposition used with spherical microphone arrays. Due to the lower number of basis functions for the partial spherical surface, a lower number of microphones is sufficient to achieve a similar spatial resolution as for a conventional spherical array over all directions. The challenges which come along with practical implementations of a partial spherical microphone arrays are discussed in detail. Based on acoustical measurements of a prototype array, the directivity of modal beamforming is investigated. To facilitate the reproduction on surrounding loudspeaker layouts with standard tech- niques, we present an approach to convert the modal representation of a partial spherical array into spherical harmonics. The performance of this conversion is evaluated using perceptually motivated error measures
Supervisors Höldrich, R.