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.