Spatiotemporal Gradient Analysis of Differential Microphone Arrays

The literature on gradient and differential microphone arrays makes a distinction between the two types, but it nevertheless shows how both types can be used to obtain the same directional responses. A more theoretically sound rationale for using delays in differential microphone arrays has not yet been given. A gradient analysis of the sound field viewed as a spatiotemporal phenomenon is presented, giving a theoretical interpretation of the working principles of gradient and differential microphone arrays. It is shown that both types of microphone arrays can be viewed as devices for approximately measuring spatiotemporal derivatives of the sound field. Furthermore the design of high-order differential microphone arrays using the aforementioned spatiotemporal gradient analysis is discussed.