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Hi all and thank you for taking time to read this.

When I read the general literature about dynamical time warping (and the vignette for the $\texttt{R}$ package $\texttt{dtw}$), the time series seem to be given at the same time index. They are not of the same length, and I do know you can do a warping that does not require the beginning and ending of the series to match, but it seems to me, that the time distance between measurements is always the same. I might be reading it all wrong, but as I see it I need two time series complying to the following in order to compare them: $$X = (X_t)_{t \in \{1,\dots n\}}$$ and $$Y = (Y_t)_{t \in \{1,\dots m\}}$$ where the time between observations $X_t$ and $X_{t+1}$ is the same as between $Y_h$ and $Y_{h+1}$ $\forall (t,h) \in \{1,\dots n\}\times\{1,\dots m\}$ (namely index 1).

However I have two time series looking like this: $$X = (X_{t_i})_{t_i \in \{t_1,\dots t_n\}}$$ and $$Y = (Y_{h_j})_{h_j\in \{h_1,\dots h_m\}}$$ where $d(t_i,t_{i+1})\neq d(h_j,h_{j+i})$ (just plain euclidean distance $d$). You could think of them both as independently randomly sampled in time. Now it seems to me that what I should do is to do some kind of interpolation of each time series separately, extract series $X'_t$ and $Y'_t$ and warp these? I can of cause (if I do not care about calculation time) make the smallest set of equidistantly sampled time points which include all my actually sampled time points - but that could be somewhat cumbersome. I guess my question is - what do you usually do? Just low key practical handling of the issue?

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So you are right that the sampling frequency needs to be constant and the same for both signals, according to the literature, https://ieeexplore.ieee.org/document/1163055. You're also right that the signals do not need to be the same length, and the ends do not need to match.

I also agree that resampling / interpolating to a smaller sampling frequency could be combersome. I have previously suggested to someone that you could convert these signals to a cumulative sum which would then be easier to interpolate to some common sampling frequency, but I don't know the result of this, and might perhaps be worth trying.


Edit: full reference for the paper added after comment request - H. Sakoe, and S. Chiba, IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume 6, Issue 1, 1978

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    $\begingroup$ please provide full reference of the paper you cite in case your link dies $\endgroup$ – Antoine 12 hours ago
  • $\begingroup$ Thanks for the comment @Antoine, added in the main text $\endgroup$ – Steven Thomas 5 hours ago

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