See the title. You could imagine that I am asking about an AM radio, but I will use a simpler example with a lock-in amplifier.
Let's say that I have a lock-in amplifier with a reference frequency of 330 Hz. If I take that signal and modulate it at 0.01 Hz and connect that to the input of the lock-in, then look at the DC output of, say, the X channel, I can see that modulation, even if the lock-in is AC coupled, with a cutoff frequency of 1 Hz (3 orders of magnitude higher).
I do not understand why this is. It seems to me to be the same as an AM radio. If you have a 500 kHz carrier frequency modulated by your signal, if you connect that to a bandpass filter, you still get your signal out, right?
So, to rephrase my question: why is the signal of interest not filtered out in both of the above cases?