Fundamentals Of Differential Beamforming (springerbriefs In Electrical And Computer Engineering)
by Jacob Benesty /
2016 / English / PDF
5.5 MB Download
This book provides a systematic study of the fundamental theory
and methods of beamforming with differential microphone arrays
(DMAs), or differential beamforming in short. It begins with a
brief overview of differential beamforming and some popularly
used DMA beampatterns such as the dipole, cardioid,
hypercardioid, and supercardioid, before providing essential
background knowledge on orthogonal functions and orthogonal
polynomials, which form the basis of differential beamforming.
This book provides a systematic study of the fundamental theory
and methods of beamforming with differential microphone arrays
(DMAs), or differential beamforming in short. It begins with a
brief overview of differential beamforming and some popularly
used DMA beampatterns such as the dipole, cardioid,
hypercardioid, and supercardioid, before providing essential
background knowledge on orthogonal functions and orthogonal
polynomials, which form the basis of differential beamforming.
From a physical perspective, a DMA of a given order is
defined as an array that measures the differential acoustic
pressure field of that order; such an array has a beampattern in
the form of a polynomial whose degree is equal to the DMA order.
Therefore, the fundamental and core problem of differential
beamforming boils down to the design of beampatterns with
orthogonal polynomials. But certain constraints also have to be
considered so that the resulting beamformer does not seriously
amplify the sensors’ self noise and the mismatches among sensors.
From a physical perspective, a DMA of a given order is
defined as an array that measures the differential acoustic
pressure field of that order; such an array has a beampattern in
the form of a polynomial whose degree is equal to the DMA order.
Therefore, the fundamental and core problem of differential
beamforming boils down to the design of beampatterns with
orthogonal polynomials. But certain constraints also have to be
considered so that the resulting beamformer does not seriously
amplify the sensors’ self noise and the mismatches among sensors.
Accordingly, the book subsequently revisits several
performance criteria, which can be used to evaluate the
performance of the derived differential beamformers. Next,
differential beamforming is placed in a framework of optimization
and linear system solving, and it is shown how different
beampatterns can be designed with the help of this optimization
framework. The book then presents several approaches to the
design of differential beamformers with the maximum DMA order,
with the control of the white noise gain, and with the control of
both the frequency invariance of the beampattern and the white
noise gain. Lastly, it elucidates a joint optimization method
that can be used to derive differential beamformers that not only
deliver nearly frequency-invariant beampatterns, but are also
robust to sensors’ self noise.
Accordingly, the book subsequently revisits several
performance criteria, which can be used to evaluate the
performance of the derived differential beamformers. Next,
differential beamforming is placed in a framework of optimization
and linear system solving, and it is shown how different
beampatterns can be designed with the help of this optimization
framework. The book then presents several approaches to the
design of differential beamformers with the maximum DMA order,
with the control of the white noise gain, and with the control of
both the frequency invariance of the beampattern and the white
noise gain. Lastly, it elucidates a joint optimization method
that can be used to derive differential beamformers that not only
deliver nearly frequency-invariant beampatterns, but are also
robust to sensors’ self noise.