Sum two plots and plot the result

Is there a simple way to take the sum of two plots that overlap and plot the result? X and Y are the same length for both.

[Rik]

The easiest way is to sum the data itself:

Z=X+Y;
plot(t,X,t,Y,t,Z)

Answer 1

[Star Strider]

One approach (assuming that they are functions of the same independent variable vector, so in addition to being the same lengths, they are evaluated at the same values of the independent variable):

XplusY = sum([X(:),Y(:)],2);

This creates a column vector result, since we don’t know the sizes of the original ‘X’ and ‘Y’. If you want it as a row vector, transpose it.

To sum only the values where ‘X’ is greater than or equal to ‘Y’:

L = X >= Y;
XL = X(L);
YL = Y(L);
XplusY = sum([XL(:),YL(:)],2);

since I am not certain what ‘overlap’ means here.

[Matthew Rotondaro]

This does not work since they are not functions of the same independent variable vector. Here, I have in one plot a set of X and Y values, and I have in the second plot X shifted by some amount and Y scaled by some amount. So the vectors remain the same lengths, but possess different values.

[Rik]

Then you will have to interpolate one or both to a shared x, after which you will be able to add them up.

[Star Strider]

If they don’t have a common independent variable, you can’t sum them and get a meaningful result.

You will have to create a common independent variable for both, then use interp1 to interpolate both of them to it. Then you could sum the interpolated curves.

Example —

Xi = linspace(1.2, 3.4, 50);
X = exp(-((Xi-2.1)/0.5).^2);

Yi = linspace(2.3, 3.4, 50);
Y = exp(-((Yi-2.9)/0.2).^2);

figure
plot(Xi, X,    Yi, Y)
grid

XiYi = [Xi(:); Yi(:)];
Ci = linspace(min(XiYi), max(XiYi), 150);
Xq = interp1(Xi(:), X(:), Ci(:), 'linear','extrap');
Yq = interp1(Yi(:), Y(:), Ci(:), 'linear','extrap');
Sq = sum([Xq(:) Yq(:)],2);

figure
plot(Ci, Xq,    Ci, Yq,    Ci, Sq)
grid

Experiment to get the result you want.

[Matthew Rotondaro]

That works! Thank you!

[Star Strider]

As always, my pleasure!

[Susmita Panda]

But the in the summation plot, the second also starts from starting rather it should have a delay?

[Niko]

What if they are both independent, i.e. same y and x "measurements", but with different density points (x-axis is more denser on one with higher resolution in a smaller window than the other)?

[Star Strider]

With respect to different independent variable ranges, the interpolation is still necessary, however they can only be summed in the ranges where all the curves exist. All the curves would need to be truncated to those limits, then the interpolated values summed, ignoring regions where they do not all overlap.

With respect to different resulutions, it is preferable to interpolate the higher resolution signal to match the values in the lower resolution signal. This avoids the problem of creating data in the lower resolution isgnal where none previously existed, as would be the problem if the lower resolution signal were interpolated to match the higher resolution signal, since the exact behaviour of the lower resolution signal at those points is obviously not known.

.

[Rik]

You might consider performing a moving average before downsampling. Otherwise you may introduce other effects (consider the situation where one of the curves is a sine and the resolution of the other curve is equal to the period of the sine).