The authors present a set of constraints for controlling the spatial derivatives of the beam pattern of a flat-response broadband processor. The constraints ensure that the beam pattern of the processor is independent of the choice of phase center location. It is shown that for the first-order case the set of constraints is linear, but for the second-order case the set of constraints is linear and quadratic. The authors then present a method for approximating the quadratic constraint with two linear constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>