Imagine I have a dataset of N spectra (eg t1, t2, ... tN), each ranging over some set of M wavelengths (e.g. 200nm-800nm). Let's say the data set has three distinct, fairly broad peaks, A, B and C. Depending on what's going on in the system, sometimes peaks change individually. For example, A will grow while B and C stay stationary. Sometimes, A and B may grow synchronously, while C stays stationary.
It's possible, but unlikely and less important, that A, B and C are all changing asynchronously, which would signify multiple underlying processes occurring simultaneously, so ignore that case.
What I'd like to do is use some sort of correlation spectroscopy techniques to show the dataset in terms of events in which only A changed. Events in which only B changed. Events where A and B changed together etc... Of course this can be done in an ad-hoc manner by going through the dataset, cropping, munging and so on, but I feel like there's got to be a defacto way to do this, and it's got to be related to available techniques in 2D correlation spectroscopy. For example, the synchronous 2D spectrum (basically the covariance) can tell me which peaks are changing together, so is there a way to filter out from the entire dataset just the timepoints when A and B are changing together? IE still have N samples, but the dataset contains some heuristic of times when A changed alone. And then in another channel, I have N samples but the heuristic shows a measure of when A and B were changing. It seems like I could use the synchronous spectra to do something like this, but don't know how.
Any ideas, even brainstorming, is helpful.
2DCorr helps you comparing two or more peaks. If you like to see the changes in single peak, collect the spectra (series) as a result of an external perturbation. Normalize the peak (in data set) of your interest with the constant peak (not changing as a function of time or temperature etc.) and create a area profile (as function of desired variable) to see the change. Repeat the same for another peak of your interest. Is that useful?
Assuming you can identify (and distinguish) the 3 peaks, you could start by representing the 3 peaks centers and standard deviation as a function of time. You would get 3 timetraces with a "sigma" band (matplotlib fill_between or similar). You can also represent amplitude or area in this way.
With this representation you can think of a model able to describe the time evolution of centers and sigmas (the same goes for the area or the amplitude).
But you can also directly perform a 1D correlation between these curves. If your experiment involves discrete events happening at specific time points, I would split the measurements and then perform the correlation.
Hope this helps.
I mean the cross-correlation between each pair of timetraces. It gives you information about the correlation, anticorrelation and after which delay a signal "follow" the other.
If there is no correlation whatsoever the cross-correlation curve will be flat.
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