Complex domain digital filter design with max-min type amplitude constraints and group delay specifications

This paper considers the design of a digital filter with prescribed magnitude and group delay specifications. Our aim is to devise suitable methods/algorithms which are useful for the design of a set of filters for multiuser communication systems. To do this, we formulate our filter design problem as a constrained L₂ space minimization problem in which the performance requirement on the group delay and magnitude in the passband are treated as constraints while minimizing the L₂ norm of the error function between the designed and the desired filters. Methods for solving the proposed nonlinear and nonconvex optimization problem are outlined. Numerical results are presented to illustrate the usefulness of the proposed method