Digital simulation of analog systems for a restricted class of inputs

A discrete system representation, H(z) is found for an analog system, H_a(ω), under certain restrictions on the class of inputs. H_a(ω) has n-poles, m-zeros, (n>;m≥0), deterministic input f(t), and output g(t). If f(t) can be represented by a finite power series expansion in [(k-1)T,kT], k=1, 2,⋯, then it is shown how to define a discrete system whose output g[k] equals the sample values of the analog output, g(kT). Each waveform element used in the series defines an n-stage digital filter. It is shown how to obtain the gain coefficients empirically from simulation or laboratory data for system identification.