Frequency invariant beamforming with exact null design

This paper extends earlier results by Ward, Kennedy and Williamson (1995, 1996) for the design of broadband arrays with frequency-invariant (FI) beam patterns to the case where it is desired to place an exact null in a given direction. The beamforming is done using appropriately selected FIR filters. First, the previous results for generating FI beam patterns using FIR filters are briefly summarised. Second, new results which give the conditions required for exact nulls in the beam pattern for all frequencies in any, possibly non-FI, beam pattern are given. Third, a method of generating beam patterns which possess an exact null and which are close, in an L₂ sense, to an arbitrary FI pattern is presented. Finally, some preliminary experimental results which corroborate the theoretical findings are presented