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On the Use of a Lebedev Grid for Ambisonics

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Ambisonics provide tools for three-dimensional sound field analysis and synthesis. The theory is based on sound field decomposition using a truncated basis of spherical harmonics. For the three-dimensional problem the decomposition of the sound field as well as the synthesis imply an integration over the sphere that respects the orthonormality of the spherical harmonics. This integration is practically achieved with discrete angular samples over the sphere. This paper investigates spherical sampling using a Lebedev grid for practical applications of Ambisonics. The paper presents underlying theory, simulations of reconstructed sound fields, and examples of actual prototypes using a 50 nodes grid able to perform recording and reconstruction up to order 5. Orthonormality errors are provided up to sixth order and compared for two grids: (1) the Lebedev grid with 50 nodes and (2) the Pentakis-Dodecahedron with 32 nodes. Finally, the paper presents some practical advantages using Lebedev grids for Ambisonics, in particular the use of sub-grids working up to order 1 or 3 and sharing common nodes with the 50 nodes grid.

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