The report presents an alternative mathematical formalism for Ambisonic directivity design in 2D and 3D using ultraspherical/Gegenbauer polynomials, differing from traditional methods. The original intention was to include these polynomials in the Ambisonics book, but the cost was too high. However, these polynomials are valuable in designing axisymmetric beams and understanding spherical designs. They are useful in spherical beamforming, and this report will explain their properties and uses. The polynomials will also be used to derive various directivity designs or Ambisonic order weightings.
Publication date: 4 Jan 2024
Project Page: https://arxiv.org/abs/2401.00813
Paper: https://arxiv.org/pdf/2401.00813
