Ambisonic Encoding of Signals From Equatorial Microphone Arrays

TL;DR

This paper adapts the equatorial microphone array's spherical harmonic encoding to produce real-valued ambisonic signals compatible with existing spatial audio tools, facilitating practical application and storage.

Contribution

It modifies the original complex-valued SH formulation to a real-valued version suitable for ambisonic applications, with an example implementation provided.

Findings

Real-valued SH representation compatible with ambisonic tools

Simplified storage and processing of sound fields in spatial audio

Practical MATLAB implementation provided

Abstract

The equatorial microphone array presented in (Ahrens et al., 2021) computes a spherical harmonic (SH) representation of a sound field based on pressure sensors along the equator of a rigid spherical baffle. The original formulation uses complex-valued SH basis functions. This is inconvenient if the SH representation of the captured sound field is intended to be stored in time domain by means of real-valued audio signals as it is common in the spatial audio format of ambisonics. The present document summarizes the modifications that need to be applied to the mathematical formulation from (Ahrens et al., 2021) to produce an ambisonic representation of the captured sound field that is compatible with the established ambisonic software tools like SPARTA and the IEM Plugin Suite. An example MATLAB script that implements this formulation is provided.