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I want to find inverse $\mathcal{Z}$ transform of

$\dfrac{2(z^2-5z+6.5)}{(z-2)(z-3)}$ valid on an annulus region for example for $2<\left|z\right|<3$

msm
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Rag
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  • Do you know how to calculate the inverse $z$-transform in general? – msm Oct 23 '16 at 11:08
  • Yeah, I know . I saw that Z transforms is defined(unilateral) for a function f(n), only when $n\geq 0$, in that case in this problem there won't be any contribution of $(z-3)$ – Rag Oct 24 '16 at 07:42
  • I left an answer @Reg. Makes sense? – msm Oct 24 '16 at 13:45

1 Answers1

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$$\dfrac{2(z^2-5z+6.5)}{(z-2)(z-3)}=2-\frac{1}{z-2}+\frac{1}{z-3}$$ we can make it more clear as $$2-\frac{z^{-1}}{1-2z^{-1}}+\frac{z^{-1}}{1-3z^{-1}}$$

Now consider the given ROC, and the table of inverse $z$-transforms, and notice that $\mathcal{Z}^{-1}\{z^{-k}X(z)\}=x[n-k]$ to find the inverse $z$-transform.

msm
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