Inverse Z Transform by Division.
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.