Effects Of Enclosure Design On The Directivity Synthesis By Spherical Loudspeaker Arrays

Spherical loudspeaker arrays have been used to generate non-uniform directivity patterns. It is known that the poor radiation efficiency of spherical sources and the loudspeaker electroacoustic behavior impose constraints on the directivity synthesis at low frequencies, which are aggravated as the source volume is made smaller. In this work, the effects of the enclosure design on the loudspeaker signal powers are analyzed. Two different approaches have been reported in literature, although quantitative comparisons have not been provided. In the first approach, the drivers share the same enclosure volume and in the second, they have their own independent sealed cavities. Here, an analytical model that takes into account the interior and exterior acoustic coupling is used in order to evaluate the voltages that must feed the array drivers. It is shown that the signal powers can be reduced at low frequencies by letting the drivers share the same enclosure volume. However, this leads to controllability problems, since some natural frequencies of the enclosure are in the operation range of the spherical array. If controllability at natural frequencies is neglected, a simple lumped parameter model of the enclosure presents good agreement with the continuous model, indicating that heavy calculations may be unnecessary.42374242Behler, G.K., Sound source for the measurement of room impulse responses for auralization (2007) Proceedings of the 19th International Congress on Acoustics, , Madrid, Spain, 02-07 SeptemberWarusfel, O., Misdariis, N., Directivity synthesis with a 3D array of loudspeakers: Application for stage performance (2001) Proceedings of the COST G-6 Conference on Digital Audio Effects (DAFX-01), , Limerick, Ireland, 06-08 DecemberKassakian, P., Wessel, D., Characterization of spherical loudspeaker arrays (2004) Proceedings of the 117th Audio Engineering Society Convention, , San Francisco, USA, 28-31 October, Paper Number 6283Zotter, F., Höldrich, R., Modeling radiation synthesis with spherical loudspeaker arrays (2007) Proceedings of the 19th International Congress on Acoustics, , Madrid, Spain, 02-07 SeptemberAvizienis, R., Freed, A., Kassakian, P., Wessel, D., A compact 120 independent element spherical loudspeaker array with programmable radiation patterns (2006) Proceedings of the 120th Audio EngineeringSociety Convention, , Paris, France, Paper Number 6783Kassakian, P., Wessel, D., Design of low-order filters for radiation synthesis (2003) Proceedings of the 115th Audio Engineering Society Convention, , New York, USA, 10-13 October, Paper Number 5925Arfken, G., (1966) Mathematical Methods for Physicists, p. 654. , Academic Press, New YorkKazhdan, M., Funkhouser, T., Rusinkiewicz, D., Rotation invariant spherical harmonic representation of 3D shape descriptors (2003) Proceedings of the Eurographics Symposium on Geometry Processing, pp. 156-164. , Aachen, GermanyBoyd, S., Vandenberghe, L., (2006) Convex Optimization, p. 716. , Ed. Cambridge University Press, Cambridge, United KingdomSmall, R.H., Direct-radiator loudspeaker system analysis (1972) Journal of the Audio Engineering Society, 20 (5), pp. 383-395Beranek, L.L., (1993) Acoustics, , Acoustical Society of America, New Yor