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I have three signals (below) each having the same standard deviation, however, are clearly very different temporally.

enter image description here

Is there some such metric that could be calculated for each of these signals to give an indication of how they vary over time, such as a measure of continuousness or intermittency if such a metric exists.

If possible, I would like to do this by calculating a single number for each of these signals, rather than windowing into smaller chunks.

Thanks

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Any metric measuring the relative importance of high-frequency content vs low-frequency content will be correlated with the amount of abrupt changes in the signal.

You can try spectral roll-off (the frequency under which x% of the energy is concentrated) or spectral centroid.

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I can't come up with any known standard measure, and it all depends on what you exactly need, but one simple measure could be computed like this:

$$M=\sum_{n=0}^{N-1}|x_{n+1}-x_n|$$

where $x_n$ is the signal of length $N$. With this measure, the top two functions would be rated similarly (one big change is similar to lots of small changes), and the bottom function would get a considerably larger value (because of its many large changes).

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