A computer method for obtaining z transforms

This correspondence gives a computer algorithm for determining the
z
transform
F(z)
of a given rational Laplace transform
F(s)
. The procedure is based on the fact that the
s
-plane poles map one-to-one into the
z
plane, so the denominator of
F(z)
can be easily determined. The numerator of
F(z)
is determined by numerically inverting the Laplace transform at the sampling instants. One advantage of the procedure is that no extra computation is required if
F(s)
has multiple poles.