What should I use for cubic function approximation/polynomial approximation?

I have a curve like spectrum that contains some noise, I like to use the principle of polynomial approximation to approximate this spectrum.

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I’m not sure what you want, but one option is polyfit. The end of the page links to necessary related functions, such as polyval.
Another option that you may be referring to is Cubic Spline Data Interpolation ( spline ).

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Thanks very much could you please explain this spline further, it looks like that will solve my problem, can I read the details of this function on MATLAB?Many thanks once again
My pleasure! The documentation for spline explains it better than I ever could.
Note that the blue type in my answer are hyperlinks, so clicking on spline in it will open the correct page in the MATLAB documentation.

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