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:


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


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 $|z|\rightarrow\infty$:


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 $0<|z|<\infty$ must be IIR.

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Yes, if all the poles are in $z=0$ then it is FIR. If not, it is IIR.

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