# Cut-off frequency for Low-pass filters in Arctangent Demodulation

According to literature, the arctan-demodulation method commonly used in Radio-frequency radar systems is the one shown below:

Is there a rule of thumb regarding the cut-off frequency of these Low-pass filters?

The primary purpose of those filters is to pass the desired signal bandwith and reject the carrier feed-through at $$\omega_h$$ and the double frequency component at $$2\omega$$. Given that, I would recommend designing the filters with a passband and rejection requirement at those frequencies in mind with a goal of minimizing filter complexity (which means maximize the transition band between passband and rejection to the extent possible). Further filtering can be done on the $$\phi(t)$$ result itself based on the video bandwidth desired.