Abstract:
Given a broadband frequency versus angle beampattern specification in the near field, a methodology is developed to yield a filter-bank design for an array signal-processing structure. This methodology relies on two key tools: (i) a transformation using spherical harmonic solutions to the wave equation which takes a near-field beampattern specification and maps it to an equivalent far-field beampattern specification for a given frequency; and (ii) a solution of the broadband frequency versus angle far-field beampattern specification problem, which generalizes earlier results on broadband frequency invariant (far field) beamforming [Ward et al., J. Acoust. Soc. Am. 97, 1023--1034 (1995)]. The transformation exploits the uniqueness property of the solution to the wave equation to give a set of truly equivalent far-field patterns for a discrete set of frequencies. There is no restriction on the bandwidth of operation beyond that imposed by limitations on the number of sensors or filter complexity. A straightforward filter-bank design is then proposed to realize this equivalent far-field broadband frequency versus angle beampattern specification. The methodology is illustrated with a broadband frequency invariant near-field design which captures the full generality of the design methodology.