3 D Audio and Applied Acoustics Laboratory · Princeton University Algorithms for Computing Ambisonics Translation Filters

In this report, we distill and reproduce the necessary algorithms for computing ambisonics translation filters. These algorithms are also described by Gumerov and Duraiswami [1, chapter 3] for complex-valued spherical harmonics and by Zotter [2, chapter III] for both complexand real-valued spherical harmonics. The translation operation consists of three steps: 1) rotating the coordinate system to align the 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 Section 1, we specify the mathematical definitions and conventions followed in this report and, in Section 2, we present a mathematical formulation of the filters for translating ambisonics signals. Next, in Section 3, we present recurrence coefficients which will be used both in Section 4 to derive the rotation matrices needed to align the z-axis and in Section 5 to derive the coefficient matrix used to translate along the z-axis. We then show in Section 6 how to combine these individual matrices in order to compute the coefficients matrix for an arbitrary translation.