Sound Field Recording by Measuring Gradients

Gradient based microphone arrays, the horizontal sound field's plane wave decomposition, and the corresponding circular harmonics decomposition are reviewed. Further, a general relation between directivity patterns of the horizontal sound field gradients and the circular harmonics of any order is derived. Based on this relation, a number of example differential microphone arrays are analyzed, including arrays capable of approximating the sound pressure gradients necessary for obtaining the circular harmonics up to order three.