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Susan my comments on SNR requirements were for binary systems. So reducing the cause of the noise is paramount (crosstalk?, ground shift? from shared current grounds , supply ripple?  unshielded vs STP wire?


After filtering to match your spectrum is ideal once you avoid the noise within your signal spectrum (like a spike).

  If 10 Hz use a 10 Hz Bessel  LPF  ( one quad Op Amp and a few discretes ) or a fancy FIR S/W filter. Over-filtering can cause errors too.


Although I cannot tell how much of your noise is not random, but there are some spikes that will  cause errors.

If lucky the noise is outside your sensor signal BW.


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