Question: 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?

Thanks!

Answer: 
> 
> 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?
> 
> 
> 

No. The original modulating waveform is filtered out. However the Amplitude Modulation process creates *sidebands* above and below the carrier frequency. If these are inside the bandwidth of the output filter then they will be preserved. When this is demodulated you get back (an approximation of) the baseband signal.

[![enter image description here](https://i.stack.imgur.com/v7JbF.gif)](https://i.stack.imgur.com/v7JbF.gif)
> 
> 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).
> 
> 
> 

A lock in amplifier actually demodulates the modulation (0.01 Hz) and presents it to you as seen on your X output. It doesn't just filter it. You cannot filter a plain ordinary AM waveform and hope to recover the baseband (modulation) without a demodulator.

Your understanding is flawed. Modulation doesn't create a baseband signal; it creates sidebands around the carrier hence, when you amplitude modulated 300 Hz with 0.01 Hz you would have sidebands at 299.99 Hz and 300.01 Hz. These easily pass through a 1 Hz filter.