Mathematical problems of synthesis of electric filters

The development of modern electronic devices often leads to meaningful mathematical statements. Two problems that traditionally arise in the synthesis of multi-band electric filters will be considered: (1) the task of approximation, i.e. finding the amplitude-frequency characteristic of the desired specification, and (2) the task of implementation is the synthesis of architecture and finding the values of the structural elements of the device implementing this characteristic. Both problems attracted the attention of the leading mathematicians of their time, E.I.Zolotarev, V.Kauer, N.I.Akhiezer, E.Stifel, A.A.Gonchar, R.Bott, and others.