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A numerical-convolution-based approach has been proposed for the accurate transient simulation of interconnects characterized by band-limited (b.l.) frequency-domain (f.d.) data and terminated by arbitrary equivalent circuits. Propagation delay is enforced in the transient results by obtaining causal impulse responses from b.l.f.d. data, extracting the propagation delays from them, and enforcing the delays in the causal impulse responses. Causal impulse responses are obtained through a new minimum- phase/all-pass decomposition of the frequency data. In this decomposition, a new form for the all-pass component has been proposed that preserves the sign of the original frequency response in the reconstructed response, unlike the prior approaches, leading to an accurate transient result. Arbitrary terminations are conveniently handled by integrating the numerical convolution in a modified nodal analysis (MNA) framework, a framework used by commercial circuit simulators, through a new transient simulation formulation. Numerical results demonstrating the accuracy and capability of the proposed procedure have been presented.