EAN: 9789811010453

SPRINGERBRIEFS IN ELECTRICAL AND COMPUTER ENGIN...

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. 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.

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