# Is it possible to digitize small signal with large noise?

I have a small signal, e.g. ~100 uV in a band of interest of 0.1 - 30.0 Hz This signal is accompnied with a huge noise of 50 Hz ~100V of amplitude.

Is it possible to digitize the small signal without the use of analog input filters to fiter 50Hz noise?

I may place an input amplifier with K = 10000. So, my small signal will be in the range of ADC's input. Input amplifier will clamp 50 Hz noise to acceptable input levels of ADC and introduce harmonics with frequencies 50 Hz and higher.
Then I will filter these harmonics with a digital filter.

• How will the signal look in the part of the waveform that is clamped? Mar 25, 2020 at 9:11
• Is it possible No, probably not. Mar 25, 2020 at 9:16
• If you scale the 100V down to fit in the 1V input range, and your ADC has a resolution of 24bits, and you manage to build your circuit so perfectly that you really get 24bits of resolution and don't add any noise, then you will be able to (barely) sample both the enormous signal and the small signal simultaneously. For all practical purposes, it will not work.
– JRE
Mar 25, 2020 at 9:20

I may place an input amplifier with K = 10000. So, my small signal will be in the range of ADC's input. Input amplifier will clamp 50 Hz noise to acceptable input levels of ADC and introduce harmonics with frequencies 50 Hz and higher

No. As soon as you allow the amplifier output to clamp, the game will be over. You are trying to dig out 100 μV of noise from 100 V of interference. Only 1ppm (part per million) offset in your interfering waveform is equal to the full range of your input signal. Any non-linear operation will mix the interference down into your baseband, and swamp it.

The one thing in your favour is that frequency separation between your wanted and unwanted signals. The first thing you need to do is use a strictly linear, by which I mean passive, filter, to reduce the amplitude of the interference. Ideally, you'd reduce it by a factor of more than 106, but that's not going to be possible with only a 30 Hz to 50 Hz ratio. You may have to sacrifice some signal amplitude at the top end of your 30Hz to get the 50Hz down. Do not even think about active filters, they do not have the dynamic range.

Start off with a high order LC elliptic filter design. This will need large values of inductor as the cutoff frequency is so low. However, the low frequencies will allow the values to be very high tolerance, necessary for getting the pass and stop bands in the right place. Ferrite based inductors can be non-linear, you may need to under-run them significantly, and test the effect.

Once the interference has been reduced to within an order of magnitude or two of your signal (I think 80dB reduction, a factor of 104, ought to be possible with an LC elliptic, leaving you 'only' a factor of 100 to go), then you can digitise, using a lot of over-sampling with respect to your 30Hz wanted bandwidth, and then recover your signal with digital filtering.

I'm making some reasonable (to me) assumptions about the noise, your requirements for signal fidelity etc in throwing these figures around. Once you've updated your question to include more detail, my numbers may have to change slightly. It's how I'd go about the task though.

(edit) On reflection, there is no way this is going to work. If the 50 Hz interference was absolutely clean a pure, then it would be possible to build a suitable filter and ADC. However, it's going to have phase noise, which will spill over into the signal bandwidth, and probably be sitting on some additive noise as well. (/edit)

• Yeah, 50Hz lowpass analog filter with high attenuation is a headache. What about an amplifier with non-constant gain? at 0 - 100 uV it will have gain fof 10000 at > 100 uV it will have gain of 0.0001 It is not so difficult to disign Mar 25, 2020 at 10:01
• An amplifier with that characteristic is called a limiter, that's little better than allowing your amplifier to clamp as in your OP. The problem is the non-constancy of your 100 V interference. Do you know what resources to use to design an LC elliptic filter? It's your only practical route. Mar 25, 2020 at 12:19
• Yes 100V is non-constant, but looks like limiting 100V sine produces only higher harmonics, which will not mix into baseband and could be filtered out by digital filter. Is it? Mar 25, 2020 at 12:28
• unfortunately that won't work, because what the limiter will be responding to is the sum of your noise and your signal, so it'll have a gain of 0.0001 any time the noise is higher than 100 μV. You'll be reducing your signal to 10 nV, and that is an even harder signal to isolate. Mar 25, 2020 at 14:04
• @XeenychXeenych Where is this 50 Hz interference coming from? Is it mains? If so, it will be so dirty as to spill noise components into your wanted bandwidth. Even if its SNR is 100dB, that's still going to give you a 20dB noise to signal ratio in the signal. Mar 25, 2020 at 14:31