smooth noisy data with spline smoothing

Hi,

I have some noisy function. See attached x and y data. I want to smooth this data and then make a derrivative of that data. When I make derrivative I get in some point Inf so I need to smooth this data. I saw in Curve fitting App that smoothing spline with center and scale option does the job which fits me but I dont quite understand how I do this in the code. I need to do it automatically for every function I'll give to do smooth so I cannot use Curve Fitting Tool every time.

Thank you very much.

Answer 1

[Bruno Luong]

See those threads can help you

https://www.mathworks.com/matlabcentral/answers/1772125-how-to-generate-a-smooth-derivative-after-fitting-a-curve-to-the-data?s_tid=srchtitle

https://www.mathworks.com/matlabcentral/answers/1925070-natural-cubic-spline-interpolation-of-y-values-how-to-get-derivative-of-the-spline-wrt-the-y-values?s_tid=srchtitle

https://www.mathworks.com/matlabcentral/answers/1894800-how-to-remove-noise-from-curves-and-take-their-derivates?s_tid=srchtitle

https://www.mathworks.com/matlabcentral/answers/276471-derivative-of-piecewise-polynomial-using-ppval?s_tid=srchtitle

[Bruno Luong]

Result with your data

x=webread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1446472/x2.txt')
y=webread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1446477/y2.txt')
x=str2num(x);
y=str2num(y);

options = struct('animation', true, 'sigma', 1e-3);
pp = BSFK(x,y,[],[],[],options); % FEX https://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation?s_tid=srchtitle_BSFK_1
pp1 = ppder(pp); % You might use fnder, I don't have the toolbox

% Check the spline model
close all
figure
xq = linspace(min(x),max(x),100);
plot(x,y,'.r',xq, ppval(pp,xq),'b')
xlabel('x')
ylabel('function y')
yyaxis('right')
plot(xq, ppval(pp1,xq), 'Linewidth', 2)
ylabel('derivative dy/dx')
grid on
legend('data', 'spline fitting','derivative','Location','north')

[Dimani4]

Thank you very much Bruno.

Actually I found the way to get the same graph as I got in the picture I attach before.

[curve, goodness, output] = fit(x2u,y2u,'smoothingspline','SmoothingParam',0.998,'Normalize','on');

P this is the smoothing parameter which runs from [0 1]. and center and scale it's I do by 'Normalize', 'on'.