# Z Transform, Inverse by expansion.

Cuthbert Nyack

If the Z transform can be expanded out as a series in powers of z, then the
coefficients of each term of the series constitutes the inverse. In the
following expression, the inverse would be the coefficients in blue.
Consider a Z transform which can be expanded as in the expression below.
Then the inverse is the coefficients in blue and can be written
as follows.
Since the final result is usually a listing of
the sample values, then this method of finding the
inverse Z transform is
usually used only as a last resort when other methods
cannot be applied.

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© 2000 Cuthbert A. Nyack.