Certified Computation of Optimal Multiband Filtering Functions

In this paper, we focus on the problem of computing multiband filtering characteristics with a guarantee on their global optimality with respect to a Zolotarev-like criterion. An iterative algorithm based on linear programming is presented. This algorithm ensures quadratic convergence to the optimal solution. We also provide an equiripple-like criterion that allows one to check in a very simple manner whether a computed filtering function is optimal or not. The latter is used to analyze two practical design examples based on asymmetric dual-band specifications. In particular, it is shown that the selectivity of the dual-band response does not necessarily increase with the filter's order. This study yields some striking results when compared to the usual single-band situation, and introduces the idea that for certain asymmetric specifications some of the filter order values are more suitable than others. Finally, the practical implementations of the filtering devices in inline dual-mode cavities and stacked single-mode cavities are detailed.