Binaural Audio Rendering in the Spherical Harmonic Domain: A Summary of the Mathematics and its Pitfalls
This work addresses the need for clarity in binaural ambisonic decoding for audio engineers and researchers, but it is incremental as it summarizes existing knowledge.
The paper reviews the mathematical framework for binaural audio rendering using spherical harmonic expansions, highlighting the importance of precise definitions to ensure consistency and compatibility with common software tools.
The present document reviews the mathematics behind binaural rendering of sound fields that are available as spherical harmonic expansion coefficients. This process is also known as binaural ambisonic decoding. We highlight that the details entail some amount peculiarity so that one has to be well aware of the precise definitions that are chosen for some of the involved quantities to obtain a consistent formulation. We also discuss what sets of definitions produce ambisonic signals that are compatible with the most common software tools that are available.