  We introduce an accurate and robust technique for accessing causality of
network transfer functions given in the form of bandlimited discrete frequency
responses. These transfer functions are commonly used to represent the
electrical response of high speed digital interconnects used on chip and in
electronic package assemblies. In some cases small errors in the model
development lead to non-causal behavior that does not accurately represent the
electrical response and may lead to a lack of convergence in simulations that
utilize these models. The approach is based on Hilbert transform relations or
Kramers-Kronig dispersion relations and a construction of causal Fourier
continuations using a regularized singular value decomposition (SVD) method.
Given a transfer function, non-periodic in general, this procedure constructs
highly accurate Fourier series approximations on the given frequency interval
by allowing the function to be periodic in an extended domain. The causality
dispersion relations are enforced spectrally and exactly. This eliminates the
necessity of approximating the transfer function behavior at infinity and
explicit computation of the Hilbert transform. We perform the error analysis of
the method and take into account a possible presence of a noise or
approximation errors in data. The developed error estimates can be used in
verifying causality of the given data. The performance of the method is tested
on several analytic and simulated examples that demonstrate an excellent
accuracy and reliability of the proposed technique in agreement with the
obtained error estimates. The method is capable of detecting very small
localized causality violations with amplitudes close to the machine precision.
