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We introduce an accurate and robust technique for accessing causality ofnetwork transfer functions given in the form of bandlimited discrete frequencyresponses. These transfer functions are commonly used to represent theelectrical response of high speed digital interconnects used on chip and inelectronic package assemblies. In some cases small errors in the modeldevelopment lead to non-causal behavior that does not accurately represent theelectrical response and may lead to a lack of convergence in simulations thatutilize these models. The approach is based on Hilbert transform relations orKramers-Kronig dispersion relations and a construction of causal Fouriercontinuations using a regularized singular value decomposition (SVD) method.Given a transfer function, non-periodic in general, this procedure constructshighly accurate Fourier series approximations on the given frequency intervalby allowing the function to be periodic in an extended domain. The causalitydispersion relations are enforced spectrally and exactly. This eliminates thenecessity of approximating the transfer function behavior at infinity andexplicit computation of the Hilbert transform. We perform the error analysis ofthe method and take into account a possible presence of a noise orapproximation errors in data. The developed error estimates can be used inverifying causality of the given data. The performance of the method is testedon several analytic and simulated examples that demonstrate an excellentaccuracy and reliability of the proposed technique in agreement with theobtained error estimates. The method is capable of detecting very smalllocalized causality violations with amplitudes close to the machine precision.

Spectrally Accurate Causality Enforcement using SVD-based Fourier Continuations for High Speed Digital Interconnects