# Calculate cut-off frequency of lowpass IIR-filter

Given a an IIR lowpass-filter in z-space:

$H(z) = \frac{\sum_{i=0}^P b_{i} z^{-i}}{1+\sum_{j=1}^Q a_{j} z^{-j}}$

How to calculate it's 3dB cut-off frequency?

I about evaluating it's fourier transform (as long it exits) and take it's magnitude:

$\frac{1}{\sqrt{2}} = \frac{|H(e^{j\omega_c)}|}{|H(e^{j0})|}$

This is then transformed to calculate $\omega_c$. Is this correct? Are there other ways to do that?

## 1 Answer

This will work but only if the it's actually a low pass filter. Your formula describes any possible IIR filter so it could really be anything.