An accurate, robust and intuitive technique to detect causality violations in broadband frequency measurements

Dispersion relations with filtering were recently proposed to reliably test the causality of sampled scattering parameters obtained with a direct measurement or a full-wave simulation. Owing to the use of a simple low-pass filter, this novel form of relations is much easier to implement and understand than previous approaches. In this paper, we demonstrate, through a rigorous theoretical analysis and numerical tests, that the novel method provides a better estimation of the detected violation. The proposed analysis also elucidates the effect of the low-pass filter on the causality test.