A Unijied Approach to the Synthesis of the Irrational Immitance

A simple method for the synthesis of irrational immittances J(Z(s)), based on infinite cascades of balanced symmetric lattices, is presented. This approach is applicable to both analog and digital implementations. The method is illustrated by physical realizations of J(L s), J( 1 /C s) and the irrational number Ja. As an obvious extension, a physical realization for the fractional-step delay z _ “* in a single-rate digital-filter structure is developed. Also, expressions for the input immittance of a truncated realization of J(Z(s)) and approximate realization of z‘I* are derived.