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 terminatedLCtwo ports. It is shown that such methods have the disadvantage that there does not exist a transformation with the three requirements that the entire imaginarys-plane axis map to thez-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 theLCfilter 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|H(e^{f{\omega}T}|is low valued throughout the passband.