Collapse/mean data in Matlab with respect to a different set of data

Question

I have two sets of data, but the sets have a different sizes. Each set contains the measurements itself (MeasA and MeasB, both double) and the time point (TimeA and TimeB, datenum or julian date) when the measuring happened.

Now I want to match the smaller data set to the bigger one, and to do this, I want to mean the data points of the bigger set around the data resp. time points of the smaller set, to finally do some correlation analysis.

Edit: Small Example how the data would look like:

MeasA = [2.7694 -1.3499 3.0349 0.7254 -0.0631];
TimeA = [0.2 0.4 0.7 0.8 1.3];

MeasB = [0.7147 -0.2050 -0.1241 1.4897 1.4090 1.4172 0.6715 -1.2075 0.7172 1.6302];
TimeB = [0.1 0.2 0.3 0.6 0.65 0.68 0.73 0.85 1.2 1.4];

And now I want to collapse MeasB and TimeB so that I get the mean of the measurement close to the timepoints in TimeA, so for example TimeB should look like this:

TimeB = [mean([0.1 0.2]) mean([0.3 0.6]) mean([0.65 0.68 0.73]) mean([0.85]) mean([1.2 1.4])]
TimeB = [0.15 0.4 0.69 0.85 1.3]

And then collapse MeasB like this too:

MeasB = [mean([0.7147 -0.2050]) mean([-0.1241 1.4897]) mean([1.4090 1.4172 0.6715]) mean([-1.2075]) mean([0.7172 1.6302])];
MeasB = [0.2549 0.6828 1.1659 -1.2075 1.1737]

Answer 1

The function interp1 is your friend.

You can get a new set of measurement for your set B, at the same time than set A by using:

newMeasB = interp1( TimeB , MeasB , TimeA ) ;

The first 2 parameters are your original Time and Measurements of the set you want to re interpolate, the last parameter is the new x axis (time in your example) on which you want the interpolated values to be calculated.

This way you do not end up with different sets of time between your 2 sets of measurements, you can compare them point by point.

Check the documentation of interp1 for more explanations and for options about the interpolation or any potential extrapolation.

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edit: Matlab doc used to have a great illustration of the function but I can't find it online so here goes:

So with the linear method, if the value is interpolated exactly between 2 points, the function will return the exact mean. If the interpolation is done closer to one point than another, the value returned will be proportionally closer to the value of the closest point.

The NaN can appear on the sides (beginning or end of returned vector) if the TimeA was not completely overlapped by timeB. The function cannot "interpolate" because there is no anchor point. However, the different options of interp1 allow you to "extrapolate" outside of the input range, or to assign another default value instead of the NaNs.