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

Bellows SD, Leishman TW. Application of Chebyshev Quadrature Rules to Equiangular Spherical and Hemispherical Directivity Measurements. J Audio Eng Soc. 2024;72(1/2):44-58. doi:10.17743/jaes.2022.0119

@article{Bellows2024_22377,
  author = {Bellows, Samuel D. and Leishman, Timothy W.},
  title = {{Application of Chebyshev Quadrature Rules to Equiangular Spherical and Hemispherical Directivity Measurements}},
  journal = {Journal of the Audio Engineering Society},
  volume = {72},
  number = {1/2},
  pages = {44--58},
  year = {2024},
  month = jan,
  publisher = {Audio Engineering Society},
  doi = {10.17743/jaes.2022.0119},
  url = {https://doi.org/10.17743/jaes.2022.0119}
}

TY  - JOUR
TI  - Application of Chebyshev Quadrature Rules to Equiangular Spherical and Hemispherical Directivity Measurements
AU  - Bellows, Samuel D.
AU  - Leishman, Timothy W.
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 72
IS  - 1/2
SP  - 44
EP  - 58
PY  - 2024
DA  - 2024/01/06
DO  - 10.17743/jaes.2022.0119
UR  - https://doi.org/10.17743/jaes.2022.0119
PB  - Audio Engineering Society
LA  - en
AB  - 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.
ER  -