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I have 2 low frequency signals on the same line that look like this:

2 signals on the same line

I would like to separate them so that I obtain the two signals that can be seen here:

enter image description here

The sampling is not perfectly intercalated, so it's not as simple as taking one point each in alternation.

I looked at ICA but my understanding is that I would need 2 recordings of the 2 mixed signals in order to separate them.

Any ideas?

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  • $\begingroup$ Assuming that you would be able to start identifying the two signals, then you might be able determine to which signal each following data point belongs to, by looking at which signal has the shortest distance to it. Maybe also include the slope, such that you can still separate the two when they cross each other. However when the two signals are very similar, then it will be hard the to separate them. Even when they diverge again, then there might be a change that data points from one signal would be assigned to the other signal and vice versa. $\endgroup$ – fibonatic Mar 7 '15 at 16:34
  • $\begingroup$ Is there a pattern in the imperfect multiplexing that could be exploited? $\endgroup$ – pichenettes Mar 7 '15 at 20:00
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You should look into a generalization of ICA called Independent Subspace Analysis (ISA). Practically it is Principal Component Analysis (PCA) followed by ICA.

There are threads on dsp.stackexchange that discuss this as well as github repos (and here) that provide various implementations.

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It would appear that the two signals are multiplexed (naive time-division multiplexing), that is to say, even-numbered samples belong to signal 1 and odd-numbered samples to signal 2 - in which case the separation is trivial. Is that the case?

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  • $\begingroup$ The question states that the two signals do not alternate, so this would not work. $\endgroup$ – fibonatic Mar 7 '15 at 19:15
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No, You need at least two mixtures (channels). Look at the reference books of the Blind Source Separation technique.

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