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Application of Chebyshev Quadrature Rules to Equiangular Spherical and Hemispherical Directivity Measurements

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Directivity measurements characterize the angular dependence of source-radiated fields, often through discrete measurements made over a spherical surface. Despite the AES56-2008 (r2019) dual-equiangular standard's ubiquity for directivity applications, no well-known spherical quadrature rule directly applies to its sampling scheme. However, this work shows how Clenshaw-Curtis--type Chebyshev quadrature rules adapt efficiently to equiangular spherical integration. Numerical experiments compare the reliability of Chebyshev, Chebshev-Lobatto, and Chebyshev-Radau quadrature rules for sampled pressure fields. The results show that significant aliasing effects do not occur until nearly twice the previously assumed limit. They also highlight the benefits of the AES approach of equivalent polar and azimuthal angle sampling intervals.

JAES Volume 72 Issue 1/2 pp. 44-58; January 2024
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