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Time warp has been widely assumed in domain of speech processing. If $Xw(t)$ represents a time warped version of $X(t)$, then $Xw(t) = X(t-w(t))$ where $w(t)$ is an arbitrary function with a banded derivation. I think it has a direct relationship with how the hearing system works in human beings.

My question is: "Is there any numerical method to verify the assumption of time warp in a set of measurement?"

I can imagine the time warp model can be proven by modeling the system which generates the signal. This is not what I mean. I am looking for a numerical method, like statistical hypothesis test or sth like that, for verifying the assumption that time warp exists.

MachineEpsilon
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Mike Zadeh
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The answer is no, statistical tests test only statistical hypotheses, your hypothesis is not really statistical.

Time wrap is an approximation, it is not really how human listening works. For example, human perfectly distinguish words with elongated vowels.

Nikolay Shmyrev
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  • Respectfully, I disagree with your definition of statistical hypothesis test. Time warp is an approximation model. The model is our hypothesis. I am interested to verify if this hypothesis is valid or not. So, if this model is accurate for specific data, the likelihood of observing data should be high. Let me put it this, you might get my question better. Let's say you work a non-speech signal, so you can get intuition from your hearing, you are interested to approximate using time warp. How do you decide that time warp assumption is valid and can be generalized? That is the point. – Mike Zadeh Apr 16 '19 at 21:28
  • Hey Mike, nice to get a comment from you ;) By "not statistical" I mean you can not really assume any distribution for your data, so you can't really get any statistics. As for verifying time wrap in an experiment, you can set this experiment for sure. Give people signals modified with wrap and ask them to distinguish them, check how reliable their judgement is. – Nikolay Shmyrev Apr 16 '19 at 23:35