A robust causality verification tool for tabulated frequency data

We introduce a robust algorithm for the qualification of tabulated frequency data representing the port responses of a linear subsystem. This algorithm is aimed at the verification that frequency responses obtained via full-wave electromagnetic simulation or from direct measurement of some interconnect structure are self-consistent and causal before they are used for the generation of macromodels for system-level analysis and design purposes. The technique is based on an advanced formulation of the Hilbert transform, leading to a direct check for causality of the raw data. One of the main advantages of the proposed method is the possibility to provide accurate estimates for error bounds due to various sources, including sampling frequency and data availability over a limited bandwidth.