Robust Causality Characterization via Generalized Dispersion Relations

The self-consistency of frequency responses obtained via numerical simulations or measurements is of paramount importance in the analysis and design of linear systems. In particular, tabulated responses with flaws and causality violations have been demonstrated to be the root cause for numerical problems and unreliability in modeling and simulation tasks. In this work, we present the generalized dispersion relations as a robust and reliable tool for the causality characterization of frequency responses. Several applications are presented, including causality and passivity verification for tabulated data and causality-controlled interpolation schemes. Practical examples illustrate the excellent performance of the proposed techniques.