6 ms·

I've found a lot of these explanations to be a lot harder to understand with words, and painfully obvious explained visually. This diagram makes it a lot simpl

I've found a lot of these explanations to be a lot harder to understand with words, and painfully obvious explained visually. This diagram makes it a lot simpler: https://www.researchgate.net/profile/Sverker_Sikstroem/publication/255630771/figure/fig1/AS:316654090244096@1452507626185/Stochastic-resonance-where-a-weak-sinusoidal-signal-goes-undetected-as-it-does-not-bring.png https://www.researchgate.net/profile/Sverker_Sikstroem/publi...

dtolnay 9y ago
The visual explanation makes it look like overlaying any sufficiently high single frequency high intensity signal would achieve the detectable threshold passing events. Is that true? Why does the article mainly focus on white noise?
- cup-of-tea 9y ago
  Yeah, I don't think the picture is correct. It's just showing how a signal can be detected even in a high noise environment by observing threshold crossing events. The article talks about the white noise resonating with the signal but not the noise. I'm trying to picture white noise as a summation of all frequencies, but I've never thought about the phase of the components. If two signals of the same frequency are in phase then they resonate, but if they are out of phase they cancel each other out. What does the phase of the components look like in white noise?
  - deusum 9y ago
    In my mind's ear you're turning up the volume until you hear the beat. After that, filter out unimportant frequencies and return the volume to normal. The important data isn't the volume necessarily, but the specific frequency and tempo.
  - mannykannot 9y ago
    The picture seems to match what the article says, with respect to a detection system having a step-like threshold. It is not a matter of the signal being detected even in a high-noise environment, as in this case, it would not be detected at all without the noise: the signal (blue) line is always below the threshold (the dotted line.) With noise added, the detector picks up the spikes above the threshold (those circled in red), and the time-sequence of those spikes has the same periodicity and phase as the original signal (plus some noise). The article points out that with too much noise, this does not work.
- mrow84 9y ago
  Your supposition seems correct to me, though I may well have misunderstood something. As for the focus on white noise, the history section in the scholarpedia article [0] suggests it's simply historical contingency. [0] http://www.scholarpedia.org/article/Stochastic_resonance#History http://www.scholarpedia.org/article/Stochastic_resonance#His...
- ivanhoe 9y ago
  Possibly because white noise has spectrum where all frequencies have equal intensity so it's easier to extract the diff created by the signal.
- mannykannot 9y ago
  Maybe it is because this example has a simple step threshold. If the response were more smoothly non-linear, perhaps using a single high frequency would lead to relatively strong intermodulation [1] artifacts at specific frequencies, while white noise generates more diffuse white-noise intermodulation. [1] https://en.wikipedia.org/wiki/Intermodulation https://en.wikipedia.org/wiki/Intermodulation
mehrdadn 9y ago
Where is the "resonance" here? What would a non-"resonating" version of adding noise to a sinusoid look like?
- IshKebab 9y ago
  I don't think there is any resonance. It's just a terrible name for it.
  - John_KZ 9y ago
    Exactly. I find it alarming that so many people make bizzare comments as if they understand nothing about basic mathematics. It feels like I'm on reddit again, and I don't want to.
  - ahartmetz 9y ago
    Yeah, reading it I was just thinking "It is dithering. Call it dithering already. DITHERING!"
    - smoyer 9y ago
      The article actually states that dithering is a different but related technique.
  - chillingeffect 9y ago
    The system I've seen it used in was Oscillatory due to regulation. A balance sensing aid for human feet. On this article they describe it as a phenomenon of bistable systems. The noise enables the oscillation.
- DanBC 9y ago
  "In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies" Which bit of this doesn't apply?
  - 9y ago

dtolnay 9y ago

The visual explanation makes it look like overlaying any sufficiently high single frequency high intensity signal would achieve the detectable threshold passing events. Is that true? Why does the article mainly focus on white noise?

cup-of-tea 9y ago
Yeah, I don't think the picture is correct. It's just showing how a signal can be detected even in a high noise environment by observing threshold crossing events. The article talks about the white noise resonating with the signal but not the noise. I'm trying to picture white noise as a summation of all frequencies, but I've never thought about the phase of the components. If two signals of the same frequency are in phase then they resonate, but if they are out of phase they cancel each other out. What does the phase of the components look like in white noise?
- deusum 9y ago
  In my mind's ear you're turning up the volume until you hear the beat. After that, filter out unimportant frequencies and return the volume to normal. The important data isn't the volume necessarily, but the specific frequency and tempo.
- mannykannot 9y ago
  The picture seems to match what the article says, with respect to a detection system having a step-like threshold. It is not a matter of the signal being detected even in a high-noise environment, as in this case, it would not be detected at all without the noise: the signal (blue) line is always below the threshold (the dotted line.) With noise added, the detector picks up the spikes above the threshold (those circled in red), and the time-sequence of those spikes has the same periodicity and phase as the original signal (plus some noise). The article points out that with too much noise, this does not work.
mrow84 9y ago
Your supposition seems correct to me, though I may well have misunderstood something. As for the focus on white noise, the history section in the scholarpedia article [0] suggests it's simply historical contingency. [0] http://www.scholarpedia.org/article/Stochastic_resonance#History http://www.scholarpedia.org/article/Stochastic_resonance#His...
ivanhoe 9y ago
Possibly because white noise has spectrum where all frequencies have equal intensity so it's easier to extract the diff created by the signal.
mannykannot 9y ago
Maybe it is because this example has a simple step threshold. If the response were more smoothly non-linear, perhaps using a single high frequency would lead to relatively strong intermodulation [1] artifacts at specific frequencies, while white noise generates more diffuse white-noise intermodulation. [1] https://en.wikipedia.org/wiki/Intermodulation https://en.wikipedia.org/wiki/Intermodulation

mehrdadn 9y ago

Where is the "resonance" here? What would a non-"resonating" version of adding noise to a sinusoid look like?

IshKebab 9y ago
I don't think there is any resonance. It's just a terrible name for it.
- John_KZ 9y ago
  Exactly. I find it alarming that so many people make bizzare comments as if they understand nothing about basic mathematics. It feels like I'm on reddit again, and I don't want to.
- ahartmetz 9y ago
  Yeah, reading it I was just thinking "It is dithering. Call it dithering already. DITHERING!"
  - smoyer 9y ago
    The article actually states that dithering is a different but related technique.
- chillingeffect 9y ago
  The system I've seen it used in was Oscillatory due to regulation. A balance sensing aid for human feet. On this article they describe it as a phenomenon of bistable systems. The noise enables the oscillation.
DanBC 9y ago
"In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies" Which bit of this doesn't apply?
- 9y ago