How to generate a smooth derivative after fitting a curve to the data?

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azarang asadi 2022-8-1

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https://ww2.mathworks.cn/matlabcentral/answers/1772125-how-to-generate-a-smooth-derivative-after-fitting-a-curve-to-the-data

评论： azarang asadi 2022-8-2

采纳的回答： Bruno Luong

Data.mat

在 MATLAB Online 中打开

Hi all,

I have a set of data which is attached. I used spline function to fit the data and then fnder to take the second derivative and my results ended to be very noisy. I tried fit(x,y,'smoothinhgspline') and I got a noisy derivative. I don't know how to find a smooth derivative. I'd appreciate your suggestions.

Here's my code:

load Data %Matt J added
% using cubic spline
pp = spline(x,y);
derX= fnder(pp,2);
yy = fnval(derX,x);
% using fit
fit1 = fit( x, y, 'smoothingspline' );
[d1,d2] = differentiate(fit1,x);

when I plot yy and d2, none are smooth, they are very noisy.

plot(x,yy,x,d2) %Matt J added

legend('Non-Smoothed','Smoothed'); %Matt J added

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Matt J 2022-8-1

I've added some lines of code and RUN output to the original post.

Torsten 2022-8-1

I get this graph for the second derivative in OCTAVE:

Sorry, it's the first derivative that I included as graphics.

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采纳的回答

Bruno Luong 2022-8-1

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https://ww2.mathworks.cn/matlabcentral/answers/1772125-how-to-generate-a-smooth-derivative-after-fitting-a-curve-to-the-data#answer_1019345

编辑：Bruno Luong 2022-8-1

在 MATLAB Online 中打开

You have to FIT the spline, not interpolate.

For example I use my own tool BSFK avalable in FEX.

load Data.mat;
pp = BSFK(x,y); % FEX 
% Check the spline model
xq = linspace(min(x),max(x),100);
pp1 = ppder(pp); pp2 = ppder(pp1); % You might use fnder, I don't have the toolbox
subplot(2,1,1)
plot(x,y,'.r',xq, ppval(pp,xq),'b')
legend('data', 'spline fitting')
subplot(2,1,2)
plot(xq,ppval(pp2,xq),'b')
ylabel('second derivative')

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Bruno Luong 2022-8-1

编辑：Bruno Luong 2022-8-1

OK attached is the script, graphical plot and MATLAB derivative data, if you find anything incoherent with the second derivative (computed by 2 ways) please let me know.

If not you can contact the author of whatever the literature you read and ask him/her to correct.