Simplified Analysis on Filtering Sensitivity Trade-offs in Continuous- and Discrete-Time Systems

TL;DR

This paper presents a simplified, explicit analysis of filtering sensitivity trade-offs in continuous- and discrete-time systems, revealing new factors influencing sensitivity integrals and validating results with numerical examples.

Contribution

It introduces a simplified analytical method that clarifies the factors affecting filtering sensitivity integrals in both continuous- and discrete-time systems, expanding understanding beyond previous complex analysis approaches.

Findings

Sensitivity integrals depend on plant and filter zeros and poles.

The analysis applies to both continuous- and discrete-time systems.

Numerical examples confirm the validity of the simplified method.

Abstract

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.