Generalization of Filtering Sensitivity Tradeoffs in Continuous- and Discrete-Time Systems: A Simplified Approach

A simplified analysis is performed on the Bode-type filtering sensitivity tradeoff integrals, which capture the sensitivity characteristics of the estimate and estimation error with respect to the process input or estimated signal in continuous- and discrete-time linear time-invariant filtering systems. Compared with the previous analyses based on complex analysis and Cauchy's residue theorem, the analysis results derived from the simplified method are more explicit, thorough, and require less restrictive assumptions. For continuous-time filtering systems, our simplified analysis reveals that apart from the nonminimum phase zero sets reported in the previous literature, the value and boundedness of filtering sensitivity integrals are also determined by the leading coefficients, relative degrees, minimum phase zeros, and poles of plants and filters. By invoking the simplified method, a comprehensive analysis of the discrete-time filtering sensitivity integrals is conducted for the first time. Numerical examples are provided to verify the validity and correctness of the simplified analysis.