Efficient time-domain simulation of frequency-dependent elements

We describe an efficient algorithm for time-domain simulation of elements described by causal impulse responses. The computational bottleneck in the simulation of such elements is the need to compute convolutions at each time point. Hence, direct approaches for the simulation of such elements require time O(N/sup 2/), where N is the length of the simulation. We apply ideas from approximation theory to reduce this complexity to O(N log N) while maintaining double-precision accuracy. The only restriction imposed by our method is that the impulse response h(t) gets "smoother" as t goes to infinity. Essentially all physically reasonable impulse responses have this characteristic. The ideas presented can also be applied to time-domain simulation of elements described in the frequency domain, including those characterized by measured data. In this paper, we demonstrate the efficiency of the algorithm by applying it to the simulation of lossy transmission lines.