# What is the ROC for this discrete signal:

$$x(k)=4[u(k-2)-u(k)*δ(k-3)]$$

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

What would the ROC be?

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

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 $(1)$?

• @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? Sep 1, 2015 at 19:09

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.

• You kind of spoiled it ... ;) Sep 1, 2015 at 19:09
• Mea cupla, mea maxima culpa. :-)
– Peter K.
Sep 1, 2015 at 19:10