How can I find inverse z transform of $$X(z)=\frac{(z-1)^{2}}{z^{3}}$$
What I did:
I am thinking to do Partial Fraction Decomposition or long division. Is there another method ?
2026-03-27 00:04:51.1774569891
Find inverse $z$-transform of $\dfrac{(z-1)^2}{z^3}$
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We have $$X(z) = \frac{(z-1)^2}{z^3} = \frac{z^2-2z+1}{z^3} = z^{-1} - 2z^{-2} + z^{-3}. $$ It follows that $$x[n] = \begin{cases} 1,& n=1\\ -2,& n=2\\ 1,& n=3\\ 0,& \text{ otherwise}. \end{cases} $$