Sensitivity of third‐ and higher‐order filters

摘要

AbstractFor any realization of a network functionF(s) =N(s)/D(s), the sensitivities that can be most readily calculated are those of the coefficients inN(s) andD(s). A simple relationship is derived that enables one to calculate the root (pole and zero) sensitivities ofF(s) in terms of the coefficient sensitivities. The root sensitivities, in turn, enable one to calculate the root pairQand root frequency sensitivities, which can be used to characterize and compare different realizations ofF(s). Application to 3rd‐ and 4th‐order filters reveals formulations that are more elegant than those already known in the literat