Study and Design of Differential Microphone Arrays

Abstract

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 al- gorithms 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 fam- ily 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 rigor- ous but yet simple theory for the design, implementation, and performance analysis of DMAs. The theory includes some signal processing techniques for the design of commonly used first-order, second-order, third-order, and also the general Nth-order DMAs. For each order, particular examples are given on how to form standard directional patterns such as the dipole, car- dioid, supercardioid, hypercardioid, subcardioid, and quadrupole. The study demonstrates the performance of the different order DMAs in terms of beam- pattern, directivity factor, white noise gain, and gain for point sources. The inherent relationship between differential processing and adaptive beamform- ing is discussed, which provides a better understanding of DMAs and why they can achieve high directional gain. Finally, we show how to design DMAs that can be robust against white noise amplification.