Convex optimization for the synthesis of matching filters

In this work we study a particular filter synthesis problem in order to minimize the reflection coefficient of the global system consisting of filter and antenna. The matching problem is formulated as an optimization problem involving the minimization of a pseudo hyperbolic distance and the solution to this problem using H
^∞
approach yields a lower bound for the matching criterion related to the computation of a matching filter, with prescribed finite degree, under selectivity constraints.