Any discrete time stable transfer function can be expressed by a discr
ete time Laguerre series with a chosen time scale. In this note, we wi
ll derive an optimum time scale such that an index is minimized. This
index ensures the coefficients of higher order Laguerre functions go t
owards zero quickly. The solution derived requires the knowledge of th
e impulse response of the discrete plant. Cases of first order plants,
second order under-damped plants and plants with multiunit delay are
also discussed.