FIR filter design with group delay constraint using semidefinite programming

Approximately linear phase FIR filters with reduced group delays are desirable in certain applications. Conventional design methods indirectly achieve the desired group delay by approximating the complex frequency response, resulting in large group delay error, especially at the vicinity of the band edge. A new design method based on semidefinite programming is proposed. An explicit expression for the group delay of an FIR filter is given. With some approximations, a linear matrix inequality constraint on group delay is formulated so that approximately linear phase FIR filters with reduced group delays can be designed using the powerful semidefinite programming approach. An illustrative design example is presented.