simplest Notch filter in the world What do you think of this notch / band reject filter for a very very narrow band ?

Original signal x[n] 
--&gt; FFT
--&gt; then I just put "0" in the FFT bin of the frequency I need to reject (notch filter)
--&gt; inverse FFT 
--&gt; output signal y[n].


How is called such a filter ? Does it really work, or is it too simple to be true ?
The frequency response of a single FFT bin filter looks like a Sinc function, which has a massive amount of overshoot or ripple at frequencies between FFT bins.  So your filter is only useful if you can strictly guarantee that the input to the FFT only contains unmodulated frequencies that are strictly and exactly periodic in the FFT aperture length (e.g. not a window on longer data of unknown periodicity or a non-periodic stream).

A notch filter is equivalent to adding the inverse of the equivalent bandpass filter to the signal.  If the bandpass has ripples, they will get added to the result of the notch, thus potentially adding a lot of noise.

So you end up with a not-so-simple (as it requires pairs of FFT computations) that likely produces terrible results.