Pseudo-passivity, sensitivity, and stability of wave digital filters

Abstract

Two basic properties of wave digital filters, their property of requiring fewer digits for the multiplier coefficients (to which the property of roundoff noise reduction is related) and their stability, had so far only been inferred from certain analogies with unit element filters. These properties are now proved in a direct way by introducing the concepts of pseudopower, pseudopassivity, and pseudolosslessness, corresponding to the familiar concepts of power, passivity, and losslessness in classical circuits.