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Fundamentals of Differential Beamforming (Paperback) (Jacob Benesty & Jingdong Chen & Chao Pan)
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This book provides a systematicstudy of the fundamental theory and methods of beamforming with DMAs, ordifferential beamforming in short. From a physical perspective, a DMA of someorder is defined as an array that measures the differential acoustic pressurefield of that order; such an array has a beampattern in the form of apolynomial whose degree is equal to the DMA order. Therefore, the fundamentaland core problem of differential beamforming boils down to the design ofbeampatterns with orthogonal polynomials. But constraints have to be consideredso that the resulting beamformer does not seriously amplify the sensors’ selfnoise and the mismatches among sensors. In this work, we first present a briefoverview of differential beamforming and some popularly used DMA beampatterns suchas the dipole, cardioid, hypercardioid, and supercardioid. Then, some backgroundknowledge on orthogonal functions and orthogonal polynomials is provided, whichforms the basis of differential beamforming. Several performance criteria aresubsequently revisited, which can be used to evaluate the performance of thederived differential beamformers. Next, differential beamforming is cast into aframework of optimization and linear system solving and it is shown howdifferent beampatterns can be designed with this optimization framework. Afterthat, several approaches are presented to the design of differential beamformerswith the maximum DMA order, with the control of the white noise gain, and withthe control of both the frequency invariance of the beampattern and the whitenoise gain. Finally, a joint optimization method is explained, which can beused to derive differential beamformers that have almost frequency-invariantbeampatterns and meanwhile are robust to sensors’ self noise.