I’m looking to analyze and compare the following `signals’:
(Edit: better renderings here: oscillations good and here: oscillations bad)
What you see are plots of neuron activations from a type of artificial neural network plotted against time. Each line in the plot is a neuron’s activation over time which can have a value between -1 and 1.
In the first plot, the activities are stable and consistent while the second exemplifies more chaotic activity (for want of a better term)– some kind of destructive interference seems to occur ever so often..
Anyhow, I would like to do some kind of ‘clever’ analysis but since signal analysis is really not my strong point, thought I’d ask for some advice here…
EDIT: Let me clarify a bit. Ultimately, I would like to characterize the data. This could for example involve the pinpointing of correlations between the individual signals contained in each plot. I would like to measure ‘regularity’ or data invariance: in the above examples, the upper plot is more regular than the lower plot. I guess therefore I could compute the variance of each signal and take that as a measure; but I was wondering if some more comprehensive signal-processing technique could be better suited (I’m not sure). In fact I’m not even sure if signal-processing is what I really want now that I think about it. Perhaps some kind of wavelet or ft analysis…
For those interested, I am working on the computational modelling of worm locomotion.
You should consult some good books on nonlinear time series analysis. For instane, a measure for the regularity of your signal could be the Lyapunov spectrum. Another possibility would entropy. If you are interested in the correlation between signal, you could use transfer-entropy or granger causality, or for neurons it would be good to have a look at some measure for phase synchronization. The bayesian stuff could also be worth trying.
But – most important – firstly you need a proper question about what you really want to know. Once you’ve got that it is far more easy to pick the right tool.
And one final hint. Look for tools outside the engineering community. Their tools are mostly linear, but you are dealing with a highly nonlinear system. Wavelets, FFT and stuff are useful if you don’t know anything about your signal and you want to have another perspective on it, but they are not suited for your kind of problem.