Regularized Linear Fractional Programming for Implementing Digital Phase Compensators

This paper describes a novel methodology for implementing allpass digital phase compensator (DPC) using the generalized linear-fractional programming (LFP) along with the regularization technique. The allpass DPC design is first stated as a generalized LFP problem, and then it is converted to a regularized minimization problem. This conversion changes the equality constraint in the generalized LFP to an inequality constraint and also adds an extra term to the objective function. The resulting problem reduces to a regularized minimization problem, which can be tackled by using linear programming (LP). That is, the regularized minimization problem reduces to an LP with only inequality design constraints. An allpass DPC example is used to demonstrate that solving the regularized LP yields an optimal solution. The design accuracy and stability issue are also revealed.