# How to describe voltage fluctuations

I am looking for a way to describe the properties of voltage fluctuations - is the RMS amplitude a suitable measure? Attached is a screenshot showing the random current fluctuations (in the case of strong noise this corresponds to a random walk)

EDIT:This random walk is the voltage fluctuations in a programmed neuron model. The "resting voltage" is $$-65mV$$ - this can also be seen as the "starting point" of the random walk. I would now like to be able to measure the "magnitude" of the fluctuations. The data vector looks like this $$v[i] = (-65,-65.12,-64.63.....$$) for i=1000 time steps, for example. But if I calculate the RMS value, I get a value that is more or less the same size as the average (i.e. 64.3mV), which is nonsensical... I may also be measuring it wrong, but according to Wiki:

$$RMS= \sqrt{\frac{1}{n}\sum_{k=1}^n x_k^2}$$

• Whether or not a particular measure is suitable depends on your problem. The RMS of the deviation from ideal would work for some problems, other problems may need a power spectral density, yet more problems may be "don't care" unless the noise peak exceeds some minimum or maximum bound. It's like asking "is it best to feed my pet seeds or bugs?" when you haven't told us if it's a mouse or a frog. Dec 26 '20 at 18:58
• @TimWescott what do you mean by the RMS of the deviation? sorry I will explain some more details: its about a neuron model, which includes noise - I want to investigate the voltage behavior for various forms and intensities of the added noise, therefore I need some robust measures
– CB95
Dec 26 '20 at 19:19
• Presumably there is some nominal voltage, and some deviation from it. The RMS value of that deviation is what I mean. To keep things in the from that Stackexchange likes, could you please Edit your question with the new information about this being from a neuron model? And perhaps tell us what aspect of the noise is important -- my point above is that you can measure noise any which way -- what's important is to measure its impact on the problem at hand. Dec 26 '20 at 22:55
• @TimWescott i habe edited the question.
– CB95
Dec 27 '20 at 8:58

Perhaps standard deviation is what you want. Standard deviation

$$\sigma= \sqrt{\frac{1}{n}\sum_{k=1}^n (x_k-x_{ave})^2}$$

(where $$x_{ave}$$ is the average of your sequence) quantifies the fluctuations of your sequence above and below the sequence's average value. The square of the standard deviation, $$\sigma^2$$, is the variance of your sequence which is a measure of the power of the fluctuations.

• can I also take the RMS of the differences x_k - x_ave?
– CB95
Dec 27 '20 at 11:48
• @CB95. If I understand your question correctly, the standard deviation is the RMS of the differences x_k - x_ave. Dec 27 '20 at 19:09
• thank you! okay then I just simply take standard deviation! But can you think of other "measures", which could be useful?
– CB95
Dec 28 '20 at 8:00
• No, not off the top of my head. It seems to me that you're interested in measuring what statisticians call "data dispersion". Perhaps you could search the Internet for "measures of dispersion". Good Luck. Dec 28 '20 at 11:14