ABSTRACT
The design of linear, time-invariant, and stable lumped-element filters is mostly based on the evaluation of real, rational transfer functions assuming that the specifications are given in the form of prescriptions for the transfer behavior of the network. This is typical for the synthesis of continuous as well as for the synthesis of digital filters. The degree of the approximating function is an essential parameter. It must be chosen sufficiently high especially to fulfil tolerance specifications. An appropriate selection of the parametrization for the functions of interest ensures that such important realizability aspects as stability and causality can be controlled easily. The design specification is described in the form of a function in the approximation interval; it is to be approximated according to an appropriate measure. The approximation problems can be solved analytically only for special characteristics; the use of tables is also limited to relatively simple specifications.
