Real-Valued Quadratic-Cone Programming for Implementing Accuracy-Enhanced Phase Filters

This paper reveals a quadratic-cone (Qcone) programming-based noniterative tactic for implementing an all-pass phase filter (APF), aiming to fit a specified ideal phase by using the APF's phase. After deriving a complex-valued frequency-response deviation function, we simplify the minimax APF design as Qcone-programming. This Qcone-programming can be solved noniteratively. That is, this Qcone-programming is a noniterative scheme, and it requires no iterations to find a Qcone-programming solution. This paper develops a new Qcone-programming formulation that only utilizes real-valued vectors and matrices. Hence, it is a real-valued Qcone-programming scheme. The last part of this paper uses an implementation example to demonstrate that this reformulated Qcone-programming scheme outperforms other existing Qcone-programming formulations in terms of the enhanced accuracy of the implemented APF.