Theory and Application of Circular Relative Harmonic Coefficients

This paper introduces a novel acoustic feature, termed circular relative harmonic coefficients (CRHC), specifically designed for circular sensor arrays. We (i) formulate the feature through a decomposition of the planar wavefield into the circular harmonics domain; (ii) derive its theoretical expression, highlighting unique properties such as frequency independence and dependence solely on source direction; and (iii) establish its direct relationship with the frequency-domain relative transfer function (RTF); and (iv) present an estimation method robust to noisy environments. These unique properties enable dominance detection and localization of a single source within mixtures containing multiple simultaneous sources. Finally, the effectiveness of CRHC for both single- and multi-source localization is validated through extensive simulated and real-world recordings.