Chebyshev optimization for the design of broadband beamformers in the near field

The use of microphone arrays for video conferences, hands-free mobile telephony and computer applications has created the demand for near-field broadband beamformer design methods. Here, a general broadband beamformer design problem is formulated as a weighted Chebyshev optimization problem, and a method to solve the resulting functionally-constrained problem is presented, The formulation can also be applied to the design of multidimensional digital finite-impulse response (FIR) filters with an arbitrarily specified amplitude and phase. Numerical results that demonstrate the minimax near-field behavior of the designed beamformers are given.