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It seems common that people assume white (aka Gaussian) additive noise. Yet it is also common to use low-pass filters to remove noise. But white noise shows up equally on all frequency bands. So it seems these two common assumptions/conventions are at odds with each other... What am I missing here?

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  • $\begingroup$ There are other types of noise. Note you yourself did not write ” Yet it is also common to use low-pass filters to remove white noise.” $\endgroup$
    – Jdip
    Commented Apr 16 at 15:47
  • $\begingroup$ Keep in mind that white noise does not exist, it's a mathematical abstraction. In real systems, different kinds of noise show up, each with different spectral properties. $\endgroup$
    – MBaz
    Commented Apr 16 at 23:04

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If your signal of interest occupies only the lower half of your observed bandwidth, but the noise added to it occupies all of it, then removing the part of the noise where no "useful" spectral energy is directly improves SNR.

So, that's what you're missing here: this low-pass filtering only makes a difference when it preserves a signal of interest more than it preserves noise.

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