Near-field broadband beamformer design via multidimensional semi-infinite-linear programming techniques

Broadband microphone arrays has important applications such as hands-free mobile telephony, voice interface to personal computers and video conference equipment. This problem can be tackled in different ways. In this paper, a general broadband beamformer design problem is considered. The problem is posed as a Chebyshev minimax problem. Using the l₁-norm measure or the real rotation theorem, we show that it can be converted into a semi-infinite linear programming problem. A numerical scheme using a set of adaptive grids is applied. The scheme is proven to be convergent when a certain grid refinement is used. The method can be applied to the design of multidimensional digital finite-impulse response (FIR) filters with arbitrarily specified amplitude and phase.