Imposing pattern nulls on broadband array responses

This paper considers the Problem of altering a quiescent design for an arra y of omni-directional sensors so that the altered design rejects afar-field broadband signal from a given direction. This problem occurs where microph one arrays are to be used to acquire speech signals for telecommunication a nd interferring signals must be rejected. Three main results are presented in this paper. First, conditions for imposing an exact broadband null upon any given quiescent array response are,derived. Second, an analysis of the sensitivity of exact nulling array responses to sensor position error is pr esented. Third, frequency domain formulations for broadband nulls are obtai ned and it is shown that these are less restrictive than the exact null con ditions which are imposed in the time domain. A Lagrange multiplier approac h is used to impose the null conditions upon a quiescent array response to minimize the square error between the quiescent and nulled responses. A des ign example is given. (C) 1999 Acoustical Society of America. [S0001-4966(9 9)02706-X].