Since a phase plane needs two variables that are dependent on time, I am thinking it can be the RR interval and the voltage variation. That is, V(t) and RR(t). What do you think? If this is possible, how to do it?
I think it is not a meaningful phase space that is constructed from V(t) and R(t)
phase space of a time series x(t) based on Taken theory is constructed from a vector [x(t-l),x(t-2*l),....,x(t-m*l] in which l is the delay and m is minimum Embedded Dimension of the time series.
Hi, Pocholo Luis Mendiola. Amin Janghorbani said correctly, but for practical purposes you can take a two-dimensional projection of the phase portrait [V (t), V (t-l)]. If you need a three-dimensional phase portrait - [V (t), V (tl), V (t-2 * l)]. Where l - constant delay, which can be defined by several ways, but the most optimal delay value is about 1/4 of the period of oscillations, in the presence of a periodic component in the analyzing signal. The main criterion for selecting the delay value l is that the resulting phase portrait was not stretched along one of the coordinates, and have more less uniform shape.
You can find more information in the book "Chaos and Nonlinear Dynamics. An Introduction for scientists and Engineers" Robert C. Hilborn:
http://www.amazon.com/Chaos-Nonlinear-Dynamics-Introduction-Scientists/dp/0198507232
Hi, Pocholo. Both Amin e Ivan said correctly. The main criterion for selecting the optimal delay value l is using a nonlinear method, for example Mutual Information. In the VRA (Visual Recurrence Analysis) or (TISEAN) Time Series Analysis software avaible, you can find more help. VRA include ECG time series data.
You can use the Hilbert transform to form the conjugate pair and thus form an analytic signal.
We usually use time delay embedding technique to reconstruct possible dynamics (phase space) from a single time series. " dimension is not wnoyght. We embedded in 4~6 dimensions.
http://www.sciencedirect.com/science/article/pii/S0960077915001344
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Delay embedding can be used for uniformly sampled data. it seems that you have non-uniform data. A simpler method but not efficient enough is to reconstruct higher-order differential of your data and plot them to see if attractor constructed or not. you can look at Gilmore works. Just note that these method can't handle noise, so in analysis use approximate construction and not exact one.
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