MATLAB: Why the first and second differential is not right after interpolation

differeitialinterpolationMATLAB

Hi everyone,
the following code shows that after an interpolation with time interval 0.01s, the first and second differential are obviously changed compared with the original countparts. the attached figures exhibit the original and interpolated data. I think after interpolation, the deviation should be small, but especially for the second differential, the variation is quite large. Could anyone show me how to make a right one? THX very much!
t1=0:0.1:2*pi;  
dt1=0:0.1:2*pi-0.1;  
ddt1=0:0.1:2*pi-0.2;  
y1=sin(t1);  
v1=diff(y1)./diff(t1);  
a1=diff(v1)./diff(dt1);  
t2=0:0.01:2*pi;
dt2=0:0.01:2*pi-0.01;  
ddt2=0:0.01:2*pi-0.02;  
y2=interp1(t1,y1,t2); 
v2=diff(y2)/0.01;  
a2=diff(v2)/0.01;
H1=figure;  
subplot(2,3,1)  
plot(t1,y1);  
subplot(2,3,2)  
plot(dt1,v1);  
subplot(2,3,3)  
plot(ddt1,a1);  
subplot(2,3,4)  
plot(t2,y2);
subplot(2,3,5)  
plot(dt2,v2);
subplot(2,3,6)  
plot(ddt2,a2);

Best Answer

Please use the following command to generate the interpolated data.
y2 = interp1(t1,y1,t2,'spline');
Using the "spline" method, the interpolated data at the query point is based on a cubic interpolation. Please refer to the following documentation for more information.
http://www.mathworks.com/help/releases/R2014a/matlab/ref/interp1.html#inputarg_method
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