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Causality enforcement via periodic continuations for high-speed interconnects
Keywords: Casualty, Dispersion Relations, High-speed Interconnects
Causality verification and enforcement is of great importance for performance evaluation of electrical interconnects. We introduce a new technique based on Kramers-Kr¨onig dispersion relations, also called Hilbert transform relations, and a construction of causal Fourier continuations using a regularized singular value decomposition (SVD) method. Given a transfer function sampled on a bandlimited frequency interval, nonperiodic in general, this approach constructs highly accurate Fourier series approximations on the given frequency interval by allowing the function to be periodic on an extended domain. The causality is enforced spectrally by imposing causality conditions on Fourier coefficients directly. This eliminates the necessity of approximating the transfer function behavior as frequency goes to infinity in order to compute Hilbert transform. The performance of the proposed method is tested using several examples including a highly non-smooth frequency response function. The obtained results demonstrate an excellent accuracy and reliability of the proposed technique. We also compare the performance of the new method with the polynomial periodic continuation approach developed by authors in [1], [2]. While using polynomial continuation, we are able to significantly reduce boundary artifacts due to the finite bandwidth of available data and the reconstruction error decreases as the smoothness of the polynomial increases, the Fourier continuation allows one to completely remove any error on the boundary by using enough Fourier coefficients with a given resolution of data [3].
Lyudmyla L. Barannyk,
University of Idaho
Moscow, ID

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