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I don't know how to formulate the question better. This question is inspired from here where the author states that satellite communication is sometimes lost when radio noise from the sun makes the signal impossible to detect.

My understanding of stochastic resonance is: A weak signal can be strengthened by adding noise, so that it can still he higher than the threshold needed to trigger detectors. The noise can be filtered out and the signal remains (this part I am not sure I understood correctly).

Why, then, does this help when we do it intentionally (add noise), but not when the noise comes from the environment? Does it have to with the frequency of the noise signal vs the frequency of the signal? Aren't we always talking about white noise?

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    $\begingroup$ the signal is not "strengthened" instead the added noise and the signal and noise are different frequency bands and the quantization error is smeared out by the added noise and that is averaged by the post-processing filter. The environmental noise does not help here because its spectrum spreads over that of the signal. The added "noise" can also be just a sine wave of the right frequency. $\endgroup$
    – hyportnex
    Commented Sep 10, 2019 at 15:16
  • $\begingroup$ @hyportnex If you turn your comment into an answer I can accept it and give proper credit in form of reputation ;-) $\endgroup$
    – kutschkem
    Commented Jan 28, 2020 at 8:09
  • $\begingroup$ Hyportnex gave a nice explanation. This is similar to the dithering noise signal processing and electrical engineers use in bit-depth conversions and sometimes in analogue-to-digital conversions to decorrelate the signal from the quantisation noise. For an introductory treatment of quantization and noise-shaping, you could check the Introduction to Signal Processing book by Orfanidis (Chapter 2). $\endgroup$
    – ZaellixA
    Commented Jan 28, 2020 at 15:36
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    $\begingroup$ @ZaellixA speaking of dithering the intuition that this works is more than hundred years old. Imagine you want to control an axle whose motion is restricted by static friction (stiction), if instead of trying to turn/stop it directly you add a little jiggle to the control signal the axle will turn a lot smoother and its motion be easier controllable than otherwise. The same idea as "stochastic resonance" but without a DARPA/Government contract... $\endgroup$
    – hyportnex
    Commented Jan 28, 2020 at 15:57

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The signal is not "strengthened" by adding extra noise to it; instead the added extra noise $N_X$ and the received signal and noise $S+N$ are in different frequency bands; when the original $S+N$ is smaller than say a quantization step then adding the right amount extra noise can make that $S+N$ flip between levels and that way the quantization error is smeared out by the $N_X$ added noise and that is averaged by the post-processing filter. The environmental noise does not help here because its spectrum spreads over that of the signal. The "added noise" can also be just a sine wave of the right frequency and right amplitude.

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