I know that directly zero DFT bins outside a frequency band has the side effect of introducing ringing, as this post says Why is it a bad idea to filter by zeroing out FFT bins?. But what about calculating the power by summing the PSD in a frequency band. In my opinion, this is similar to first setting the out-band PSD amplitudes to zeros (which may cause ringing in time domain) and then summing the remainning nonzero amplitudes.
I guess it is different from first applying a bandpass filter to the time domain signal(which has no ringing) and calculating the power by averaging the squared time domain samples. Can you point out how much error the frequency domain method has? or maybe these two methods are equivalent?