A direct optimization method for low group delay FIR filter design

This paper studies the design of FIR filter with low group delay, where the desired phase response is not being approximated. It is formulated as a constrained optimization problem, which is then solved globally. Numerical experiments show that our design method can produce a filter with smaller group delay than that obtained by the existing convex optimization method used in conjunction with a minimum phase spectral factorization method under the same design criteria. Furthermore, our formulation offers us the flexibility for the trade-off between the group delay and the magnitude response directly. It also allows the feasibility of imposing constraints on the group delay.

► A direct optimization method is proposed to solve the design of FIR filter with low group delay.
► A sufficient condition is presented to identify the global minimizer of the proposed constrained optimization problem.
► A SDP-based algorithm is proposed to solve the dual problem.