open_system('vdp_1')
open_system('vdp_2')
[t1,xout1] = sim('vdp_1');
[t2,xout2] = sim('vdp_2');
x1 = xout1(:,2);
x2 = xout2(:,2);

Quick test for equality

Do a quick test for equality between variables using isequal.

isequal(x1,x2)

ans =
     0

This gives you a fast way to cycle through tons of data and turn up the subset that requires further investigation.

For a sanity check, I think it is natural to plot the data to see if the difference is visible.

plot(t1,x1,t2,x2)
legend('Sim1','Sim2')

This is actually rarely helpful for small differences in signals. In this case, the green line is on top of the blue line, so they must be the same, right? Well, they must be the same at least to the resolution of my monitor. Depending on the reason you are comparing these signals, you might stop here, but if you need more precision, how about looking at the difference?

plot(t1,x1-x2)

Computing the Absolute Difference

If signals are periodic, and the error is cumulative, the difference will generally also be periodic. I am often trying to evaluate if the difference is growing in magnitude or shrinking. I usually look at the absolute difference between signals.

x_diff = abs(x1-x2);
plot(t1,x_diff)

If you want a difference measure, you could imagine that your solution is a vector in a high dimensional vector space. I imagine the difference between the solutions to be the magnitude of the difference. To compute this, you might use the norm

nx = norm(x1-x2)

nx =
  1.5108e-012

Because I often see a wide range of differences in signals, I think it is better to use a logarithmic scale in the plot. When differences enter into a system on the order of eps, and grow larger, the logarithmic scale will help draw attention to the small magnitude differences as much as the larger magnitude differences.

semilogy(t1,x_diff,'.-')
set(gca,'YGrid','on')

Now it's your turn

When do you compare signals? How do you do it? Leave a comment here and share your technique.

Get the MATLAB code

Published with MATLAB® 7.10