Synthesis of leapfrog‐type digital filters based on the distributed circuitsimulation

It is known that a leapfrog‐type digital filter obtained by simulating an LC ladder filter terminated with resistors on both ends is a digital filter with a low coefficient sensitivity. In this paper, an analog circuit to be simulated is chosen as a distributed circuit in which the real frequency and the discrete variable correspond rigorously. By means of an equivalent transformation, a leapfrog‐type digital filter is constructed in which no delay free loop is generated. In this method, an LC ladder circuit expressed in terms of the Richard variable p is transformed to the circuit expressed in terms of the LDI variable γ. the digital filter is configured by simulation of the relationship between the node voltage and series branch current in each element of LC ladder circuit. However, if the configuration is based on general distributed LC ladder circuits, a delay‐free loop is always generated and configuration becomes unstable. As a solution to this problem, unit elements are introduced in this paper. It is shown that a realizable signal‐flow graph can always be obtained if stub circuits are used as the original circuit. the basic section necessary to circuit configuration is presented. Finally, as a practical example, the present method is used for design of a fourth‐order bandpass filter. the results are described and compared with those by other configurations.