I would like to know when I can determine that a system is stable. I've seen Stability of a system but this is very theoretically. My background is that I've set up a measurement system to detect the signal changes of a gas sensor. Means, when I add such and that of a gas the sensor will change accordingly.

But when do I state that the signal I observe is stable? Per eyeballing it isn't that hard but I would like to use a better, more reproducible characteristic. A common thumb of rule is fine.


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    $\begingroup$ A system can be stable (as in that a bounded input signal never leads to unbounded output), a signal can't be. It's not a term that is applicable to signals. $\endgroup$ – Marcus Müller May 27 '20 at 9:59
  • $\begingroup$ Thanks for the correction. I guess system and signal is quite convertible here? Or in other words: When is the system, represented by a signal, stable? When I only see the signal I have to use this as reference. $\endgroup$ – Ben May 27 '20 at 10:04
  • $\begingroup$ I'd argue that this is exactly the point where they are not convertible! But let's move forward here: I think you mean that this signal is the impulse response of your LTI system, is that right? $\endgroup$ – Marcus Müller May 27 '20 at 10:13
  • $\begingroup$ In that case, this answer answers your question with the harsh truth that an LTI system is stable if the integral over the absolute impulse response is finite – there's no thumbier rule than that! $\endgroup$ – Marcus Müller May 27 '20 at 10:15
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    $\begingroup$ There's a terminology collision here, exacerbated by the fact that a lot of signal processing beginners don't understand what system stability means. Are you, in fact, asking how to determine when your signal has settled out? (Which is more or less a synonym of "stable" in the sense of "not moving", but doesn't overlap with "stable" in the systems sense of "doesn't move without external input") $\endgroup$ – TimWescott May 27 '20 at 15:12

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