Robust Causality Check for Sampled Scattering Parameters via a Filtered Fourier Transform

We introduce a robust numerical technique to verify the causality of sampled scattering parameters given on a finite bandwidth. The method is based on a filtered Fourier transform and includes a rigorous estimation of the errors caused by missing out-of-band samples. Compared to existing techniques, the method is simpler to implement and provides a useful insight on the time-domain characteristics of the violation. Through an applicative example, we shows its usefulness to improve the accuracy of macromodeling techniques used to convert sampled scattering parameters into transient simulation models.