Cyclic alternance

The synthesis of optimal electrical filters (analog, digital and microwave) is based on the solution of a certain rational approximation problem in the uniform norm, which is a generalization of the fourth Zolotarev problem. This problem has projective invariance, which was previously ignored in the alternanation characterization of the problem's solution. An overview of the state of research in the filter problem will be given, and in particular, a projective version of the alternanation theorem will be proposed.