Time-Domain Implementation of Broadband Beamformer in Spherical Harmonics Domain

Most of the existing spherical array modal beam-formers are implemented in the frequency domain, where a block of snapshots is required to perform the discrete Fourier transform. In this paper, an approach to real-valued time-domain implementation of the modal beamformer for broadband spherical microphone arrays is presented. The microphone array data are converted to the spherical harmonics domain by using the discrete spherical Fourier transform, and then steered to the look direction followed by the pattern generation unit implemented using the filter-and-sum structure. We derive the expression for the array response, the beamformer output power against both isotropic noise and spatially white noise, and the mainlobe spatial response variation in terms of the finite impulse response (FIR) filters' tap weights. A multiple-constraint problem is then formulated to find the filters' tap weights with the aim of providing a suitable tradeoff among multiple conflicting performance measures such as directivity index, robustness, sidelobe level, and mainlobe response variation. Simulation and experimental results show good performance of the proposed time-domain broadband modal beamforming approach.