How reduce data from 3917x2 to 1868x2 without change the entire of graph?

I have zdata.mat contains data 3917x2 I need a way to reduce data to 1868x2 , (hint: first column refers to x axis, second column refers to y axis)

[Bajdar Nouredine]

thank you dear

Answer 1

[John D'Errico]

Just take every other data point, if you just want to roughly reduce the size. But you say you want a specific length. So then you would need to interpolate.

load zdata.mat
plot(z(:,1),z(:,2),'-')

x = z(:,1); y = z(:,2);
xnew = linspace(min(x),max(x),1868);
ynew = interp1(x,y,xnew);
length(ynew)

ans = 1868

plot(xnew,ynew,'-')

Finally, if you want to do some smoothing, you might try something like:

ysmooth = smooth(x,y);
ynewsmooth = interp1(x,ysmooth,xnew);
plot(xnew,ynewsmooth,'-')

And depending on the smoothing method you choose, you can adjust the amount of smoothing done. You could also use a smoothing spline. Something like this (fit requires the curve fitting toolbox.)

spl = fit(x,y,'smoothingspline');
ynewspl = spl(xnew);
plot(xnew,ynewspl,'-')

Remember that when you have a sharp spike as this curve shows, anything you do to downsample such a curve may miss exactly where that spike happens, and how far it extends. But that is a given. If you reduce the sampling frequency, then you also reduce the information content of your data.

[Walter Roberson]

First it is necessary to verify that the points are equidistant. Which they do happen to be, to within reasonable tolerance.

format long g
load zdata
unique(diff(z(:,1)))

ans = 14x1

0.870986465779879 0.870986465779993 0.870986465780106 0.870986465780334 0.870986465780902 0.870986465780959 0.870986465781016 0.870986465781925 0.870986465781982 0.870986465782039

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diff(unique(diff(z(:,1))))

ans = 13x1

1.0e+00 * 1.13686837721616e-13 1.13686837721616e-13 2.27373675443232e-13 5.6843418860808e-13 5.6843418860808e-14 5.6843418860808e-14 9.09494701772928e-13 5.6843418860808e-14 5.6843418860808e-14 7.84439180279151e-12

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eps(z(end,1))

ans = 
      4.54747350886464e-13

Hmmm, the maximum difference is 16 or 17 times the maximum epsilon, so in theory we should be reinterpolating over a constant difference.

[John D'Errico]

Note that interp1 makes no presumption of a uniform stride between data points. This is also the case for fit, which does not give a hoot about uniformity of stride. Finally, while SOME of the methods offered in smooth do care, not all of them do.

[Walter Roberson]

My note about the differences was after your original answer, but before you did the interpolation.