A Generalized Design Method for Directivity Patterns of Spherical Microphone Arrays

Enzo De Sena, Hüseyin Hacıhabiboğlu and Zoran Cvetkovic
Department of Informatics, King's College London Strand,
WC2R 2LS, London, United Kingdom

Spherical microphone arrays provide a flexible solution to obtaining higher-order directivity patterns, which are useful in audio recording and reproduction. A general systematic approach to the design of directivity patterns for spherical microphone arrays is introduced in this paper. The directivity patterns are obtained by optimizing a cost function which is a convex combination of a front-back energy ratio and a smoothness term. Most of the standard directivity patterns - i.e. omnidirectional, cardioid, subcardioid, hypercardioid and supercardioid - are particular solutions of this optimization problem with specific values of two free parameters: the angle of the frontal sector, and the convex combination factor. By varying these two parameters, more general solutions of practical use are obtained.

Here you can access the Mathematica notebooks implementing what is described in the paper.

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1) GDDP for I order microphones [Mathematica Notebook] [Video]
2) GDDP for II order microphones [Mathematica Notebook] [Video]
3) GDDP for III order microphones [Mathematica Notebook] [Video]