
Stochastic Resonance - caseymarquis
https://en.wikipedia.org/wiki/Stochastic_resonance
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united893
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/publi...](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)

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dtolnay
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?

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cup-of-tea
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?

~~~
mannykannot
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.

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pgt
This is essentially signal normalization. Sensor systems operate on a narrow
band of inputs using non-linear components (like e.g. diodes). Adding noise is
like raising the DC voltage on a signal so that it shifts the signal to within
your operating parameters. For example, for a transistor amplifier to work,
the base diode needs a 1.4V difference to turn on and amplify a 10mV source
signal.

What makes white noise interesting is that it has a zero DC component (on
average) by randomly adding energy as often as it subtracts, while passing
through analog components (like a capacitors where R(s) = 1/(sC) in s-domain).
In my view, this is still a form of amplification.

Adding Gaussian noise around your source frequency is certainly source
amplification because it's equivalent to attenuating the surrounding "noisy"
frequencies for the benefit of your sensor equipment. This would increase the
signal-to-noise ratio, but you have to know what the base frequency is you are
trying to measure.

I hope to be corrected by the signal folks, but it seems misleading to me that
"the frequencies in the white noise corresponding to the original signal's
frequencies will __resonate __with each other, " when resonance does not occur
in the signal, but in the resonant body of the sensor, and so this is more
about sensor system calibration than boosting an unknown source signal.

It seems that the practical implications are that you can have simpler sensors
(that work in a narrower band) if you can cheaply control the input noise
based on sensor reading.

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peppery
This is a richly intriguing phenomenon, with interesting implications!

For those interested in reading more, this article (on stochastic resonance's
potential importance in biological sensing) is edifying:
[https://www.physik.uni-
augsburg.de/theo1/hanggi/Papers/282.p...](https://www.physik.uni-
augsburg.de/theo1/hanggi/Papers/282.pdf) (Hänggi, Peter. "Stochastic resonance
in biology: how noise can enhance detection of weak signals and help improve
biological information processing." ChemPhysChem 3.3 (2002): 285-290.)

(Perhaps this is an example of how biological systems can value accurate
sensation so highly that they invent ingenious sensing schemes to achieve high
performance.)

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gugagore
I've heard the term "dithering" used for this, in electronics and a sort of
related (reverse?) idea in displaying images on low color depth displays. I
think. For example if you have a DAC generated 8-bit data, but you want finer
resolution, then you could imagine averaging maybe every pair of samples,
which if you add (and divide by two) the samples, you get an extra bit of
information.

But that only works if your signal (including the measurement circuit) is not
rock steady, which would make both samples identical and so you don't gain any
information. Adding noise helps the samples be different which can increase
the effective resolution. If you were just on the brink of a discretization
bucket, a kick of noise will likely push you into the next bucket

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DiabloD3
Dithering isn't the reverse idea, but maybe more of an inverse idea. Instead
of adding noise to produce more signal, you add noise to reduce artifacts
(unwanted signal in your signal).

Dithering exploits the human senses, so maybe in a way it _is_ the same thing,
just for the meatware in our heads.

~~~
gugagore
That's how I meant it. Your eye, optics, and nerves too probably, make
averaging happen. Noise gets averaged.

Not sure what distinction you are making between inverse and reverse, but I'm
curious.

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ahartmetz
If you find this interesting, another cool (and also badly named - "resonance"
would actually make some sense for that one!) measurement technique for even
tinier signals is lock-in amplification.

The idea isn't very complicated, but the Wikipedia explanation is god-awful.
I'll try: You modulate the cause of the signal you want to measure with some
sine function of frequency f. Then you take the resulting signal and multiply
it with the clean sine function of frequency f. You integrate (sum up) the
result of that over a long time. Incredible sensitivity (and very slow
reaction to changes) results.

If you know what a convolution is, the explanation can be shorter.

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John_KZ
Adding noise just amplifies the total signal intensity, allowing it to exceed
a threshold for detection. It's not really amplification, and there's no real
resonance. You cannot have a signal resonate with random noise, mixing an 8
bit signal with 8 bits of noise gives you less than 2^-40 chance of resonating
for more than 10 cycles. The name is a flawed way of describing a signal
processing technique.

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notMick
Nice, though, you could probably get better performance by using an analogue
integrator and sigma Delta encoding. Probably even better if you down convert
(multiply with expected frequency first) You can swap bandwidth for
resolution.

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badrabbit
Doea anyone know if there have been any attempts to see if this effect can be
used to detect anomalous log events that get drowned out by all the noisy
logs?

