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If I am sampling a sensor with white noise (Johnson) that is the noise floor of the system could I drive the noise floor down by sampling a larger bandwidth than I care about and then using a digital brick wall filter to remove the unwanted frequencies? I am trying to spread the noise power of the sensor across a larger frequency range so that I can have a lower noise floor in a small bucket. I think what I am proposing is similar to noise shaping techniques but I want to apply them to Johnson noise instead of quantization noise.

Example picture of system. Trying to reduce the Johnson noise impact from the 10Meg

enter image description here

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  • $\begingroup$ Are you using an any sort of anti-aliasing filter? Could you edit your question with a diagram of your system, showing the sensor, any pre-ADC signal conditioning, and the ADC? $\endgroup$
    – TimWescott
    Mar 22, 2022 at 23:54
  • $\begingroup$ @TimWescott added. I am interfacing an ADC directly to some sensor with 10Meg output resistance (Johnson noise) and trying to detect the smallest signals I possibly could from the sensor voltage source. For the purposes of discussion let's assume my ADC can be set to any sampling rate and bit depth. $\endgroup$
    – EasyOhm
    Mar 23, 2022 at 0:13

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I don't see any obvious way how this could work.

Since your noise is white, whenever you double the bandwidth you also double the noise power so you will just collect more noise and not more useful information. The signal to noise ratio in the band of interest stays the same.

Noise shaping requires access to the actual noise signal. For a quantizer, that's not a problem since you can easily calculate the quantization noise. You can't apply this to noise that's already part of your signal.

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