Design of stable symmetric and non-symmetric half-plane digital recursive filters

A method for the design of half-plane recursive filters is presented. The method is based on the construction of a 2V analog network with positive and negative reactive elements in one variable s1, positive reactive elements in the other variable s2, resistors and gyrators. The denominator Δ(s1,s2) of the driving point function of this network, which is shown to be mixed-min phase polymomial in s1,s2for all possible values of the network elements, is used along with double bilinear transformation to obtain stable half-plane recursive filter transfer functions. A design example for the case of non-symmetric half-plane filter is given.