Inverse Z Transform by Division.

Cuthbert Nyack
If analytical methods are not readily applicable for finding the inverse Z transform, then one can resort to dividing the numerator by the denominator. Analytical formulas are available for the general term.
Here it is assumed that G(z) represents the transfer function of a system and finding the inverse transform is identical to finding the unit impulse response of the system. G(z) is therefore converted to a difference equation and the numerical values of the terms found assuming the input is a unit impulse.

The numerical values calculated are plotted and shown in the applet below for different values of a to h. The applet also illustrates the final value theorem.

When enabled, the following gif file show how the applet should appear. The yellow x shows the final value according to the final value theorem agreeing with the asymptotic steady state values obtained for the inverse Z transform.

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2007 Cuthbert Nyack.