# Finite duration vs infinite duration sequences?

What are difference between finite duration and infinite duration sequences? As far as i am able to google and know only one difference that is finite duration sequence ROC exist on xy plane while infinite duration sequence ROC exist on unit circle plane

I have also attached two snapshots in this regard

There is a slight misunderstanding here. There is no such plane called unit circle plane. Unit circle is in the xy plane (or we call it z plane). The difference is, rather, in the shape of the ROC. For infinite duration sequences, the ROC is in the form of a circular strip in the xy plane (as shown in the second figure).

In the case of finite duration sequences, ROC is the entire xy plane except at z=0 or at z = $$\infty$$ or at z=0 and $$\infty$$.

e.g. $$x(n) = \{1,\underset{\uparrow}{2},3\}$$

$$X(z) = \sum \limits_{-\infty}^{+\infty} x(n)z^{-n}$$

$$= x(-1)z^1+x(0)z^0+x(1)z^{-1} = z+2+\frac{3}{z}$$

This Z transform will not exist only if $$z=\infty$$ (for the first term) and $$z=0$$ (for the last term). This can be generalised for all finite duration signals that their ROC consists of entire z plane (xy plane) except at z=0 or z=$$\infty$$ or at both.

• Do we also have a circular strip ROC in s domain just like we have in z domain as you told? – engr Mar 3 '20 at 6:28
• Yes. In s domain, we have a strip that is parallel to the y axis of the s plane. – Shehin Mar 3 '20 at 7:10
• "strip that is parallel to the y axis of the s plane" Will that strip be circular/ring shaped? or you mean that strip is imaginary(y axis) itself? – engr Mar 3 '20 at 9:57
• I couldn't understand :"This can be generalised for all finite duration signals that their ROC consists of entire z plane (xy plane) except at z=0 or z=∞ or at both." If ROC consists of either z=0 or z=∞ ,but not both,will our signal be considered finite duration or infinite duration in that case?? – engr Mar 3 '20 at 10:08
• For a right sided finite signal, ROC is the entire z plane except z=0 and for a left sided finite signal, ROC will be entire z plane except z=$\infty$. For a two sided finite signal, ROC will be the entire z plane except both z=0 and z=$\infty$ . The example I have given is a two sided case. – Shehin Mar 3 '20 at 10:29