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The visual explanation makes it look like overlaying any sufficiently high single frequency high intensity signal would achieve the detectable threshold passing

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

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