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If a signal contains deterministic, stochastic as well as chaotic components, does this generally represent a problem in the analysis of the signal? By a problem, I mean that a signal containing all three components should be considered a special case, and that it should be analyzed with the help of some specified theory/method.

A specific example I am considering is the Center-of-pressure signal generated by data from a pressure platform. One of the few concrete descriptions of the difficulty related to this signal states that the presence of deterministic, stochastic and chaotic components in the COP signal may result in mixing up the different behaviors of COP with each other. Again, I am unsure whether this problem arises more generally or if it is specific to the COP signal.

EDIT : We want to compare two or more signals with each other. The point is to look for differences in quantities such as amplitude/velocity over time. E.g ; we might analyze the signal data, and extract the path amplitude. I should further mention that this signal is also non-linear by nature, if it has significance to the matter.

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  • $\begingroup$ Welcome to SE.SP! Can you say a little more about what you’re trying to extract from the signal? Please edit your question to add anything that might help. $\endgroup$
    – Peter K.
    Feb 19, 2022 at 14:43
  • $\begingroup$ That depends. As a first cut, if the chaotic part of the signal can be ignored, or if it can be modeled as a stationary random signal, then you just do that and don't worry that it's "not really random". $\endgroup$
    – TimWescott
    Feb 19, 2022 at 17:44
  • $\begingroup$ No I dont think so. It is by nature irregular so much like a 3d pendulum for example. The point is ultimately to compare very small fluctuations in two or even more time series developments. I'm not really well versed in the terminology of this field, so I'm having a hard time expressing the problem clearly. $\endgroup$ Feb 19, 2022 at 20:42
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    $\begingroup$ "Chaotic" means deterministic but with high sensitivity to changes in initial condition. Specifically, two or more instances having the exact same initial conditions will follow the same path every time. But if they are inexact, they will differ relatively quickly. How quickly is dependent on Lyapunov exponents. By comparing two signals, you will be trying to determine if they have similar initial conditions. The stochastic part generally means you will have uncertainty in your estimation which could be quantified if the process is described accurately by some model (e.g. WGN). $\endgroup$
    – Ash
    Feb 21, 2022 at 4:36

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