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$$ x(k)=4[u(k-2)-u(k)*δ(k-3)]$$

I found that the $\mathcal{Z}$ transform of the signal is $X(z)=4/(z^2)$.

What would the ROC be?

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  • $\begingroup$ Is this homework? If so, label it with the homework tag. $\endgroup$
    – Peter K.
    Commented Sep 1, 2015 at 18:26
  • $\begingroup$ No, it's not homework, school hasn't started yet. It's just an exercise i'm trying to solve. $\endgroup$
    – angie
    Commented Sep 1, 2015 at 19:01

2 Answers 2

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HINT:

Remember that the ROC is the region in the $z$-plane for which the series

$$X(z)=\sum_{n=-\infty}^{\infty}x[n]z^{-n}\tag{1}$$

converges. Since you've found $X(z)$ you also know that $x[n]=4\delta[n-2]$, i.e. there's only one value of $n$ for which $x[n]$ is not equal to zero. What does that mean for the convergence of $(1)$?

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  • $\begingroup$ @angie: No, the ROC has nothing to do with $n$, it's about the allowed values of $z$. So for which values of $z$ does the "series" $\ldots+0+0+4z^{-2}+0+0+\ldots$ converge, that means have a finite value? $\endgroup$
    – Matt L.
    Commented Sep 1, 2015 at 19:09
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So the $\mathcal{Z}$ transform is $4z^{-2}$ so that the actual signal is $4\delta[n-2]$. From this table, that means that the ROC is all of $z$ except the origin.

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    $\begingroup$ You kind of spoiled it ... ;) $\endgroup$
    – Matt L.
    Commented Sep 1, 2015 at 19:09
  • $\begingroup$ Mea cupla, mea maxima culpa. :-) $\endgroup$
    – Peter K.
    Commented Sep 1, 2015 at 19:10

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