FIR or IIR filter from poles and zeros Is it possible to differentiate between FIR and IIR Filter just by knowing the poles and zeros of the system? 


If yes, how? 
If not, why?


Thank you.
Axel Mancino's answer is correct for causal filters. In general, FIR filters have poles at either $z=0$ or $|z|\rightarrow\infty$, or both.

Take as an example a fourth-order causal FIR filter:

$$H_1(z)=a+bz^{-1}+cz^{-2}+dz^{-3}+ez^{-4}\tag{1}$$

Clearly, $H_1(z)$ has all its poles at $z=0$. An anti-causal FIR filter such as

$$H_2(z)=az^4+bz^3+cz^2+dz+e\tag{2}$$

has all its poles at $|z|\to\infty$. And, finally, a general non-causal FIR filter has poles at $z=0$ as well as at $|z|\rightarrow\infty$:

$$H_3(z)=az^2+bz+c+dz^{-1}+ez^{-2}\tag{3}$$

In sum, a filter with all its poles at $z=0$ or $|z|\to\infty$ (or both) is an FIR filter. Filters with poles in the region $0&lt;|z|&lt;\infty$ must be IIR.