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 output tends
to have a frequency-dependent response. One exception, perhaps, is the
family of differential microphone arrays (DMAs) who 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. 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,
cardioid, supercardioid, hypercardioid, subcardioid, and quadrupole. The
study demonstrates the performance of the different order DMAs in terms
of beampattern, directivity factor, white noise gain, and gain for point
sources. The inherent relationship between differential processing and
adaptive beamforming 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.
