Second-order-cone-programming scheme for designing all-pass phase systems

This paper proposes a new method for designing digital all-pass phase systems based on the second-order-cone-programming (SOCP) formulation. Since the second-order-cone (SOC) constraint matrix contains an unknown parameter (phase peak-error), we shrink the search inverval containing this unknown parameter by applying the bi-section search scheme until the minimum error is found, which leads to the final phase-system coefficients. An example is provided to validate this feasibility-check-based design scheme.