Circular microphone array with tangential pressure gradient sensors

Abstract

Microphone arrays have already been successfully applied to record sound fields. They are typically composed of pressure sensors and different designs have been suggested, each trying to overcome practical difficulties, such as transducer noise, spatial aliasing and non-uniqueness of the inverse solution. Typical designs are of spherical (3D) or circular form (2D) and use pressure sensors. The array corpus is usually either solid or as acoustically transparent as possible. In this paper, the theoretical model of a circular microphone array, observing the tangential component of the pressure gradient on its boundary is presented.

Theoretical Study of Acoustic Circular Arrays With Tangential Pressure Gradient Sensors

“…This result was presented before in [1] and is also very similar to what Meyer described in principle for dipole sensors aligned with a circumferential orientation on the equator of a sphere [17].…”

“…An initial study of this design was presented by the authors in reference [1]. This work complements the initial work with further theoretical and numerical in-depth analysis, as well as with an investigation of the noise and aliasing performance and the array's optimal frequency band.…”

“…The equation (1) as given in [25], describes the acoustic pressure at an arbitrary position as a linear superposition of an infinite number of plane waves travelling into all possible directions , where is a unitary vector.…”

“…In theory, this is potentially not satisfied; however, the order truncation discussed in Section III ensures that this condition is always satisfied. Finally, the explicit expression of the solution is (29) It follows from (27), (29) and (12) that the series coefficients are given by (30) Equations (29) and (30) have already been presented in [1] but they were derived from a Singular Value Decomposition instead. The result in (30) is very similar to that given in (13).…”