  A simplified analysis is performed on the Bode-type filtering sensitivity
trade-off integrals, which capture the sensitivity characteristics of the
estimate and estimation error with respect to the process input and 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 non-minimum 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 on 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.
