Synthesis of digital ladder filters from LC filters

Digital ladder filter networks may be realized by applying simple transformations to the flow-graph network representation of continuous domain resistively terminated two ports. It is shown that such methods have the disadvantage that there does not exist a transformation with the three requirements that the entire imaginary -plane axis map to the -plane unit circle, that the resultant discrete network is stable and finally that the resultant discrete network be computationally realizable due to Its freedom from delay free loops. A synthesis technique is proposed for low sensitivity digital ladders. The conventional transformation that is applied to the filter prototype does lead to a stable structure with the required mapping property; the delay free loops are eliminated by straightforward flow-graph manipulation. The coefficient sensitivity of the magnitude transfer function is low valued throughout the passband.