Spherical harmonic analysis of equalization in a reverberant room

In this paper, we investigate the performance of acoustic equalization in reverberant environments. We first highlight an efficient general representation of a sound field using spherical harmonics. We then use this representation to develop a concise closed-form expression for robustness of equalization to sensor movement. This expression is used (i) to characterize equalization performance for a general class of non-isotropic sound fields and (ii) to quantify the improvements to equalizer robustness that can be obtained by using a directional microphone. The approach used here does not use any of the assumptions of statistical acoustics, but instead exploits the inherent properties of a sound field as described by the wave equation.