Nearfield broadband array design using a radially invariant modal expansion

This paper introduces an efficient parameterization for the nearfield broad band beamforming problem with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the ac tual broadband beampattern shape. The parameterization is based on an ortho gonal basis set of elementary beampatterns by which an arbitrary beampatter n can be constructed. A set of elementary beamformers are then designed for each elementary beampattern and the desired beamformer is constructed by s umming the elementary beamformers with frequency and source-array distance dependent weights. An important consequence of our result is that the beamf ormer can be factored into three levels of filtering: (i) beampattern indep endent elementary beamformers; (ii) beampattern shape dependent filters; an d (iii) radial focusing filters where a single parameter can be adjusted to focus the array to a desired radial distance from the array origin. As an illustration the method is applied to the problem of producing a practical array design that achieves a frequency invariant beampattern over the frequ ency range; of 1:10 (which is suitable for speech acquisition using a micro phone array), and with the array focused either to farfield or nearfield wh ere at the lowest frequency the radial distance to the source is only three wavelengths. (C) 2000 Acoustical Society of America. [S0001-4966(00)03901- 1].