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Based on \begin{equation} x(-t) \rightarrow {X}(-\omega) \hspace{1cm} (time-reversal) \end{equation} \begin{equation} {x^*}(t) \rightarrow {X^*}(-\omega) \hspace{1cm} (conjugation) \end{equation} if we were able to split a function $x(t)$ into real/imaginary parts and then further into even/odd functions, \begin{equation} x(t) = {x_R^E}(t) + {x_I^E}(t) ...

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The DTW approach is applicable to signals where there is an acceleration or deceleration between the observations of similar signals during the data capture and will show how similar or not the signals are besides the distortion from the "time-warping". I am not sure that would be the best approach for this case given nothing is indicating there will be a ...

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I'm not an expert in this area but I can think of Add random noise to a 40-Hz sine wave: ts = std*randn(1,N) + sin(2*pi*40*t) Add a random phase: phi = std*randn(1,N); ts = sin(2*pi*40*t + phi)

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I probably wouldn't bother interpolating at all. You want to downsample by factor 128 anyway, so from that point of view, your raw data is already a good approximation of being uniformly sampled at 128Hz. Just go with low pass filtering and downsampling and you should be good. Try it on a small fraction of the data, to get an idea of the error you introduce ...

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