How to Average Graphs with Different Time Indices?

[u-zara]

I have 10 sets of data which I have to analyze. The data represents a change in voltage over time and I want to come up with an "average" curve to represent the 10 sets of data. The problem is that the time index for each data is different so I can't simply average the voltage. Is there any method which I can use to solve this problem? I've attached an image of the graph with 3 sets of the data so you understand what I'm dealing with. Thanks in advance.

 

[Simon Bridge]

I take it you have reason to believe that the three plots are for the same physics?

The time index does not matter - just combine the three plots as a single set of ordered pairs (v,t). The time step t_i-t_i-1 need not be constant.

 

[u-zara]

Thanks for the reply. However I'm not just thinking of combining the graphs. I want a curve which is an average of all the data, for example a single spline curve which represents the data.

 

[Number Nine]

Thanks for the reply. However I'm not just thinking of combining the graphs. I want a curve which is an average of all the data, for example a single spline curve which represents the data.

That sounds suspiciously like a regression problem, but approaching it that way is going to be a little complicated (e.g. the errors are clearly not normally distributed).

 

[Simon Bridge]

Yeah - it's very skewed.

Is there any method which I can use to solve this problem?

... and what problem was that?

The problem is that the time index for each data is different so I can't simply average the voltage.

... that's right, you need to use a weighted average.

As Number-Nine says, this is a regression problem with non-normal statistics.
You can, however, use the physics of the situation to guide the shape of the regressed curve - and then you have to decide what sort of regression you will be happy with.

Of course, you can just make a guess to the curve and adjust the parameters by eye until you get something reasonable. The human visual system is quite good at this sort of thing but you may have to be more rigorous than that.

 

[haruspex]

It's a bit hard to tell from the fog of datapoints, but it looks to me that the time axis problem is worse than merely having different sample instants; some of the datasets look stretched in time relative to others. Is that what you meant when you said the time index was different?