Infinite-dimensional SVD for revealing microphone array's characteristics

Nowadays, many acoustical applications utilize microphone arrays whose configurations have a lot of varieties including linear, planar, spherical and random arrays. Arguably, some configurations are better than the others in terms of acquiring the spatial information of a sound field (for example, a spherical array can distinguish any direction of arrival, while a linear array cannot distinguish the direction perpendicular to its aperture direction due to the rotational symmetry). However, it is not easy to compare arrays of different configurations because each array has been treated by a specific theory depending on the configuration of the array. Although several criteria have been proposed for evaluating and/or designing the arrays, most of them are application-oriented criteria, and the best configuration for some criterion may not be a better one for the other criterion. Therefore, an analysis method for microphone arrays which does not depend on the array configuration or application is necessary. In this paper, the infinite-dimensional SVD is proposed for analyzing and comparing the properties of arrays. The singular values, functions and vectors obtained by the proposed method provide the fundamental properties of an array.