# Find the frequency of a pole (Discrete Form) [closed]

I am studying a Notch filter. I found its Transfer Function (in Z) and its poles. How can I find the frequency of theses poles (which corresponds to the cut-off frequency)?

Thank you very much for your help

• Welcome to DSP.SE! A notch filter doesn't have a "cut-off frequency" as such. It has a single frequency that it aims to nullify. Is that the frequency you are trying to find? – Peter K. Nov 4 '15 at 20:30

$$N(z)=z^2-2\cos(\omega_0)z+1\tag{1}$$
You can verify that this polynomial has two complex conjugate zeros at $z=e^{j\omega_0}$ and at $z=e^{-j\omega_0}$, so the notch frequency is given by the normalized angular frequency $\omega_0$.