Unconstrained Minimax Design of Cascade-Form Allpass Phase System

Abstract

Since implementing a high-order digital system using low-order systems has many advantages such as low coefficient-quantization sensitivity and high implementation modularity, this paper formulates the optimal design of a high-order digital phase system by cascading several second-order allpass sections. For a prescribed ideal phase response, the phase system design seeks to find the optimal coefficient values of all the cascaded second-order sections, which is a nonlinear optimization problem. This paper finds the optimal coefficient values through minimizing the worst-case phase error without imposing any stability constraints on the design formulation. Instead, the stability of the designed high-order phase system is confirmed by checking the stability of all the second-order allpass sections. An example is presented in the paper for demonstrating the design accuracy as well as for checking the stability.