What kind of Interpolation Algorithm Will be Applicable for the Following data set to obtain smooth curve?

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suraj karki 2022-10-27

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https://ww2.mathworks.cn/matlabcentral/answers/1837593-what-kind-of-interpolation-algorithm-will-be-applicable-for-the-following-data-set-to-obtain-smooth

评论： suraj karki 2022-10-27

采纳的回答： Bruno Luong

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Hello there,

I have a following data set,

x =     
[443.0000  443.9000  482.0000  496.6000  560.0000  561.4000  654.6000  664.5000  703.9000  740.2000  782.5000  835.1000  864.7000  864.8000  1608.9000  1613.7000  2200.7000  2202.4 ]
y =     
[1.0464  1.0641  0.9832  0.9631  0.9370  0.9358  0.9611  0.9574  0.9820  0.9955  1.0287  1.0034  1.0021  1.0063  1.0372  1.0336  1.0343  1.0290 ]

This plot represents the actual data set

Now I was doing shape preserving interpolation

In this case, this type of interpolation following the actual data, At this point I want to perform different interpolation algorithm which helps to smoothing the interpolating data set.

Could you please share any idea?

Thank you.

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John D'Errico 2022-10-27

编辑：John D'Errico 2022-10-27

If the algorithm changes the data (i.e., smooths it) then it is not interpolation.

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Answer 1

Bruno Luong 2022-10-27

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https://ww2.mathworks.cn/matlabcentral/answers/1837593-what-kind-of-interpolation-algorithm-will-be-applicable-for-the-following-data-set-to-obtain-smooth#answer_1085633

编辑：Bruno Luong 2022-10-27

在 MATLAB Online 中打开

It looks like your data has a couples of pairs/tripples that are closely spread.

I suggest to merge thme to a single point then fit the data that are merged.

x = [443.0000 443.9000 482.0000 496.6000 560.0000 561.4000 654.6000 664.5000 703.9000 740.2000 782.5000 835.1000 864.7000 864.8000 1608.9000 1613.7000 2200.7000 2202.4 ];

y = [1.0464 1.0641 0.9832 0.9631 0.9370 0.9358 0.9611 0.9574 0.9820 0.9955 1.0287 1.0034 1.0021 1.0063 1.0372 1.0336 1.0343 1.0290 ];

[xu,~,J]=uniquetol(x,10,'DataScale',1);

xi=linspace(min(x),max(x),500);

yu=accumarray(J(:),y(:),[],@mean);

yi=interp1(xu,yu,xi,'makima');

plot(x,y,'or',xi,yi,'b');