Low frequency sound spatial encoding within an enclosure using spherical microphone arrays

In a spherical coordinate system, interior sound field can be expressed in terms of a series of Fourier-Bessel expansions. The process that obtains the expansion coefficients by use of a microphone array (e.g., a spherical microphone array) is called spatial encoding. Until now spatial encoding has mainly been examined in a free field or a diffuse field which can be modeled as a sum of plane waves. For spatial encoding within an enclosure at low frequencies, special challenges would be encountered in two aspects. First, the expansions are influenced by array configurations. Second, an acoustic mode based model instead of a plane wave based one should be considered. This study focuses on these challenges. Different kinds of array configurations were compared specifically at low frequencies, and the spatial encoding for the cylindrical cavity modes was investigated. It was found that the spherical array with cardioid microphones was optimal when k r < 1, the cavity modes can be effectively represented by only a sparse subset of expansion coefficients and a good reproduction can be achieved even outside the spherical valid region, which demonstrates an effective alternative way to describe the cylindrical cavity modes and can be implemented efficiently in practice.