Introduction -- Problem Formulation -- Study and Design of First-Order Differential Arrays -- Study and Design of Second-Order Differential Arrays -- Study and Design of Third-Order Differential Arrays with Three Distinct Nulls -- Minimum-Norm Solution for Robust Differential Arrays -- Study and Design of Differential Arrays with the MacLaurin’s Series Approximation.

Microphone arrays have attracted a lot of interest over the last few decades since they have the potential to solve many important problems such as noise reduction/speech enhancement, source separation, dereverberation, spatial sound recording, and source localization/tracking, to name a few. However, the design and implementation of microphone arrays with beamforming algorithms is not a trivial task when it comes to processing broadband signals such as speech. Indeed, in most sensor arrangements, the beamformer tends to have a frequency-dependent response. One exception, perhaps, is the family of differential microphone arrays (DMAs) that have the promise to form frequency-independent responses. Moreover, they have the potential to attain high directional gains with small and compact apertures. As a result, this type of microphone arrays has drawn much research and development attention recently. This book is intended to provide a systematic study of DMAs from a signal processing perspective. The primary objective is to develop a rigorous but yet simple theory for the design, implementation, and performance analysis of DMAs.