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Suppose i have all my poles in unit circle center. What kind of information this gives me?

Can i determine if this filter is IIR or FIR?

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If you have $N$ poles at $z=0$ this means that your transfer function has the form

$$H(z)=\frac{P(z)}{z^N}\tag{1}$$

where $P(z)$ is a polynomial. What does this tell you about the filter type? (Hint: write $H(z)$ as a sum of positive and negative powers of $z$).

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  • $\begingroup$ If you put it that way, it must be FIR filter, because Z^-13 = 1. $\endgroup$ – eimvs Nov 10 '20 at 21:48
  • $\begingroup$ @eimvs: Not sure if I understand your reasoning, but the conclusion is correct. $\endgroup$ – Matt L. Nov 11 '20 at 7:49

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