z-domain synthesis of discrete-time reactance functions

Discrete-time images of lossless LC one-port ladder networks are presented. Such images are obtained by expanding discrete-time reactance functions into z-domain continued fractions to obtain the discrete-time counterparts of Cauer-1, Cauer-2, and mixed-Cauer expansions. A methodology for synthesis of discrete-time reactance functions similar to the one known for the synthesis of a continuous-time reactance function in the s-domain is presented. The type of reactance functions used is related to the continuous-time counterpart by the lossless-discrete-integrator (LDI) s-to-z transform. Simple first- and second-order discrete-time reactance networks using delay elements, multipliers, and adders are proposed and used in a step-by-step procedure to realize higher-order networks. The methodology is valid for any discrete-time reactance function using any of the three z-domain Cauer expansions, giving rise to three different ladder structures. An algorithm for the computer implementation of the synthesis procedure is developed and a BASIC listing is given