Abstract
This paper demonstrates that microphone array design can be achieved within a universal methodology of mathematical optimization. Both farfield and nearfield microphone array problems are formulated in terms of convex optimization formalism. In farfield array design, array weights are optimized to tradeoff Directivity Index (DI), White Noise Gain (WNG) and the coefficient norm. In nearfield array, convex optimization is applied to design Equivalent Source Method (ESM)-based Nearfield Acoustical Holography (NAH). Numerical examples are given in designing a farfield random array comprised of thirty microphones. Five design approaches, including a Delay-And-Sum (DAS) beamformer, a Super Directivity Array (SDA), three optimal arrays designed using 1 , 2 , and ∞ -norms, are compared. It was seen from experiments that sufficient WNG is crucial to robust performance of the arrays against sensor mismatch and noise. For nearfield arrays, inverse filters were designed in light of ESM and convex optimization to reconstruct the velocity fields on a baffled spherical piston source. The proposed method is benchmarked by conventional Tikhonov Regularization (TIKR) and the Truncated Singular Value Decomposition (TSVD). Overall, these methods have attained comparable performance of reconstruction of surface velocity in nearfield imaging.