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how to remove noise from curves and take their derivates

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This question was flagged by Image Analyst
Hello,
I have some curves which are not smooth, I have to take their derivative. therefore first requirement is remove the noise and take the derivative.
I am doing this work through curve fitting using rat35, poly9 etc. and then taking the derivative. but everytime i run the script, result changes slighty.
i am attaching the curve , their zoom version and then warnings which appeared in workspace, would you please guide me how i should handle this issue.
Regards,
Kiran

Accepted Answer

Bruno Luong
Bruno Luong on 16 Jan 2023
Edited: Bruno Luong on 16 Jan 2023
I would chose spline fitting rather than polynomial (bad) or rational.
Look at the shape of your data, I doubt any simple analytic model can fit it well.
c=readtable('100_li_4th_discharge1.xlsx');
x=table2array(c(:,1));
y=table2array(c(:,2));
% https://fr.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation
pp=BSFK(x,y,[],[],[],struct('sigma',1e-9,'KnotRemoval','none'));
ppd=ppder(pp); % derivative
xi=linspace(min(x),max(x),1024);
figure
h1=plot(x,y,'.g',xi,ppval(pp, xi),'r');
yyaxis right
h2=plot(xi,ppval(ppd,xi),'k')
legend([h1; h2],'data','fit','derivative');
  3 Comments
Bruno Luong
Bruno Luong on 17 Jan 2023
Edited: Bruno Luong on 17 Jan 2023
ppd is dy/dx, if you want dx/dy it is 1./ppd.
BTW in this case you could fit x vs y instead of the opposite.
c = readmatrix('https://fr.mathworks.com/matlabcentral/answers/uploaded_files/1265640/100_li_4th_discharge1.xlsx')
Q=c(:,1);
V=c(:,2);
% https://fr.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation
pp=BSFK(V,Q,[],[],[],struct('sigma',1e-9,'KnotRemoval','none'));
ppd=ppder(pp); % derivative
yi=linspace(min(V),max(V),1024);
figure
h1=plot(V,Q,'.g',yi,ppval(pp, yi),'r');
xlabel('V')
ylabel('Q')
yyaxis right
h2=plot(yi,ppval(ppd,yi),'k')
legend([h1; h2],'data','fit','derivative');
ylabel('dQ/dV)*')

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More Answers (2)

Matt J
Matt J on 16 Jan 2023
Edited: Matt J on 16 Jan 2023
If you provide a StartPoint in your fit options, the warning will go away and the fit will be the same when you rerun.
However, the differences you see with each run are not meaningful. You get a slightly different result because the start point of the iterative fitting process is different each time, but in this case they all seem to be converging to essentially the same curve.
  6 Comments
Matt J
Matt J on 16 Jan 2023
Edited: Matt J on 16 Jan 2023
Use a lower order polynomial so that the parameter estimates won't be as sensitive. Or use a non-polynomial model. Image Analyst suggested an exponential fit. A smoothing spline might also work,
Basically, you should experiment with other models to see if a stiffer model would work.

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Image Analyst
Image Analyst on 16 Jan 2023
You can use sgolayfilt, which is a sliding polynomial fit within the sliding window, however if I were going to take the derivatives of your curves, I'd fit them to an exponential decay (to get a formula with numerical coefficients), which has a known derivative. See my attached exponential decay demo which uses fitnlm. I have many other functions fit with fitnlm, so it you want them, just ask.

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