Introduction - Study and Design of Differential Microphone Arrays - page 10

acoustic environment and then being corrupted by some unwanted noise. A
DMA consisting of M microphones is used to pick up the signals. To estimate
the source signal, the M noisy signals are partitioned into small overlapping
frames of a few milliseconds. Each frame is transformed into the short-time
Fourier transform (STFT) domain. In each subband, a differential beam-
former is designed and applied to the multichannel signals, thereby produc-
ing an estimate of the clean signal spectrum in this subband. Finally, the
time-domain clean speech estimate is constructed using the overlap-add or
overlap-save technique with the inverse STFT. Apparently, the most crucial
step in this paradigm is the design of the differential beamformers, which is
one of the main focuses of this topic.
The problem addressed in this work is of great importance from both the
theoretical and practical viewpoints. From the theoretical side, it is essen-
tial to understand the theory and principles underlying DMAs from a signal
processing perspective. On the practical side, DMAs can be used in a wide
range of applications such as teleconferencing, hands-free communications,
3D sound recording, mobile phones, hearing aids, bluetooth headphones, and
navigation systems in cars, just to name a few. Therefore, it is important to
understand the design issues of DMAs and their limitations as well as the
way to circumvent those limitations.
1.3 Organization of the Topic
The material in this topic is organized into seven chapters, including this
one. In the next six chapters, we attempt to cover the most basic concepts
and fundamental techniques used in the design and implementation of the
different orders of DMAs and the associated beamforming algorithms. All
is explained from a signal processing perspective. The material discussed in
these chapters is as follows.
Chapter 2 presents the general formulation of a DMA design problem. It
also introduces several basic concepts that are important and useful in the
design and evaluation of a DMA including the steering vector (for a plane
wave with the conventional anechoic and farfield model), the beampattern,
the gain in SNR, the white noise gain, the directivity factor (the SNR gain in
diffuse noise), etc. In the design of a DMA, a particularly structured matrix
called the Vandermonde matrix generally appears (explicitly or implicitly) in
the formulation. This matrix and its inverse is also discussed.
The simplest form of a DMA is the first-order one that uses only two
omnidirectional sensors. If the two microphones are properly placed, many
beampatterns, such as the dipole, cardioid, subcardioid, hypercardioid, and
supercardioid, can be formed by processing the two microphones' outputs.
Chapter 3 is dedicated to the design of first-order DMAs. It discusses how
to form different beampatterns and studies the performance associated with