Design of Complex FIR Filters with Group Delay Constraints Using Second-Order Cone Programming

This paper proposes a new method for the design of complex coefficient finite impulse response (FIR) filters with group delay constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is used in this study for the optimal minimax design of linear-phase and low-delay FIR filters. The proposed approach imposes a non-convex group delay constraint which can be formulated as a second-order cone constraint with reasonable approximations. Simulations are presented to illustrate the performance of the proposed algorithms.