All-pass digital system design using second-order cone programming

In this paper, we propose a new approach for designing an all-pass (AP) digital filter that approximates a given ideal phase response in the minimax error sense. Originally, such a design problem is highly non-linear and difficult to solve. This paper formulates the non-linear problem as a second-order-cone programming (SOCP) problem and then solves the design problem using any SOCP-solver (software). After the SOCP-based design is formulated, the AP filter coefficients can be easily found through solving the SOCP problem. As compared with the existing linear programming (LP) design, the SOCP-based design method achieves more accurate fitting. A design example is given for illustrating the performance improvement of the SOCP-based design approach.