Accurate minimax design of variable fractional-delay filters using linearized octagonal constraints

This paper proposes a linear programming (LP)-based minimax design of even-order finite-impulse-response (FIR) variable fractional-delay (VFD) digital filters. The original minimax design is a non-linear optimization problem. To convert this non-linear problem into a linear one, we apply the rotation theorem to linearize the non-linear constraints as linear ones through constraining the complex-valued errors of variable frequency response (VFR) inside an octagon in the complex plane such that the resulting constraints are linear functions of the VFD filter coefficients. Hence, the minimax design can be done by using an LP technique. An example is given to illustrate that an even-order VFD filter can be designed more accurately than using the decoupling LP approach that solves a pair of LP sub-problems separately.