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I have two sets of signals. This is how they look

Signal 1

enter image description here

Signal 2

enter image description here

It seems just by observing them that Signal 1 is a little more choppy (fluctuating) that Signal 2. But I want to be sure. Can someone suggest a mathematical way by which I could characterise the choppiness of these signals?

Black Dagger
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    You need to measure the noise spectra. If the "choppiness" is white noise and if the distribution is gaussian, then you can calculate an rms noise value. Part of the problem with your question is that it's not clear what these short series are supposed to represent. Without knowing what generates these signals one can't make a reasonable theory for their stochastic behavior, either. – CuriousOne Aug 03 '16 at 08:47
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    @CuriousOne These signals represent wing amplitudes of two flies. One is flying stably (signal 2) and the other is not (signal 1) – Black Dagger Aug 03 '16 at 08:54
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    This seems like it's off topic here, but it might be on topic at [dsp.SE]. We can migrate it there if others agree. – David Z Aug 03 '16 at 08:54
  • That's cute! :-) Are we looking at one period of the movement or is this already the envelope as a function of time? The reason why I am asking is because a simple rms calculation will have serious problems with signals like the fifth diagram of signal 2. There is obviously a large "drift" that exceeds the actual noise term. One would usually try to model this base signal, remove it and then analyze the residuals, but that, as I said, requires a dynamic model. – CuriousOne Aug 03 '16 at 09:00
  • @BlackDagger to add to what CuriousOne suggested: if i can tell correctly these are MATLAB plots. the spectrum is then easily obtained from your raw data by using the FFT function on your raw data: http://uk.mathworks.com/help/matlab/ref/fft.html In case there are no obvious features to distinguish the two signals plotting the FFT on a loglog scale sometimes helps. So summarising my suggestion is: try this and observe what you see :) – Wolpertinger Aug 03 '16 at 09:12
  • @Numrok thanks I was thinking the same. But why do you suggest a log-log scale? – Black Dagger Aug 03 '16 at 09:14
  • @BlackDagger it may not be useful in your specific situation. usually noise has some sort of power law frequency spectrum with a lot of fluctuation in the detail. the power law trend becomes a lot more visually obvious amongst all the fluctuations when plotting loglog. it's really just a trick to get out the information from the spectrum. i would plot both loglog and normal and see which one is more useful maybe. you might find more high-frequency components for signal 1. – Wolpertinger Aug 03 '16 at 09:17
  • @ Just one more things. I don't know the exact sampling frequency of the signal. I know it's approx 220 Hz. Can I do a fft with an approximate value of sampling frequency. – Black Dagger Aug 03 '16 at 09:37
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    It's not clear to me that you know enough about the signal to make any useful statements about it. Separating noise and signal requires that one has models for both and then we can do a fit and determine if the hypothesis that the combined noiseless model plus the noise model are statistically consistent with the data. With short datasets like the ones in your diagram an FFT will produce nothing but artifacts. You really need to find out how the data was taken and you need to get your hands on the raw data set. The one you have seems processed, already. – CuriousOne Aug 03 '16 at 10:09
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    I'm voting to close this question as off-topic because it would be more appropriate on another SE site, namely Signal Processing. – sammy gerbil Aug 03 '16 at 13:30

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