A projective view of the problem of a multiband electrical filter

The filter is an electronic device (depending on the version it can be analog, digital or microwave), which suppresses the incoming signal on the given stop bands and passes it with little distortion of the amplitude on the pass bands. The synthesis of such an instrument is based on solving a certain problem of rational approximation in a uniform norm, reminiscent of the third problem of Zolotarev. A new look at the formulation of problems in this area will be offered and the recent successes in solving this problem related to the use of the Ansatz method are described.