Authors: Tylka, J. G., Choueiri, E. Y.
Publication: 3D3A Lab Technical Report #2
Date: March 5, 2019

Algorithms for computing ambisonics translation filters can be computed using the recurrence formulae derived for spherical Fourier-Bessel translation coefficients. These algorithms were originally described by Gumerov and Duraiswami (2005) for complex-valued spherical harmonics and by Zotter (2009) for both complex- and real-valued spherical harmonics. The translation operation consists of three steps:

1. rotating the coordinate system to align the (vertical) z-axis with the desired translation direction,
2. translating along the new z-axis, and
3. rotating the coordinate system back to its original orientation.

In this report, we distill and reproduce the necessary algorithms for computing these ambisonics translation filters.