Binaural Audio Rendering in the Spherical Harmonic Domain: A Summary of the Mathematics and its Pitfalls

TL;DR

This paper reviews the mathematical foundations of binaural audio rendering using spherical harmonic coefficients, emphasizing the importance of precise definitions for consistent ambisonic decoding and software compatibility.

Contribution

It clarifies the mathematical details and potential pitfalls in binaural ambisonic decoding, providing guidance for consistent implementation.

Findings

Highlights the importance of precise definitions in mathematical formulations

Identifies potential pitfalls in binaural rendering with spherical harmonics

Provides recommendations for software-compatible ambisonic signals

Abstract

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.