Identification of microwave filters by analytic and rational H2 approximation

In this paper, an original approach to frequency identification is explained and demonstrated through an application in the domain of microwave filters. This approach splits into two stages: a stable and causal model of high degree is first computed from the data (completion stage); then, model reduction is performed to get a rational low order model. In the first stage the most is made of the data taking into account the expected behaviour of the filter. A reduced order model is then computed by rational H2 approximation. A new and efficient method has been developed, improved over the years and implemented to solve this problem. It heavily relies on the underlying Hilbert space structure and on a nice parametrization of the optimization set. This approach guarantees the stability of the MIMO approximant of prescribed McMillan degree.