Extract (splined) function from two vectors

Hi, I have the following plot and want to extract an expression for an exponential function that's located slightly below the plotted line. Is it possible to do this in Matlab somehow?

Regards

David

Answer 1

[Matt J]

If you just want to do a polynomial fit, polyfit would be enough

    p=polyfit(x,y,2);

Because the spikes will interfere with the fit (by any algorithm), you might want to do a second pass, removing the outliers,

    keep=(y-polyval(p,x))<2e-4;

    p=polyfit(x(keep), y(keep), 2);  %refinement

Or you could do a pre-pass over the data with a median filter.

Answer 2

[Ahmet Cecen]

This might sound like a simple-minded suggestion, if you are looking for a function "slightly below" the one you drew, why not just subtract a "slight" margin from the y-axis (like y-0.0001) then find a regular exponential fit using cftool or fit.

[David]

I think that those two Matlab functions just plot that line in the figure? I want to find the mathematical function for that line on the form: f(x)=a*x^2+b*x+c

[Ahmet Cecen]

Firstly, those two functions will give you the explicit formula of your fit. Secondly, f(x)=a*x^2+b*x+c is a polynomial, not an exponential. Use cftool, choose your x and y, then chose the polynomial fit to be second degree. Look at the left of the plot and you'll see the coefficients of the fit. If you don't have the statistics toolbox, then you can use my MultiPolyRegressV3 function at the file exchange, although it won't do the plotting of the actual curve for you, it will find you your coefficients for polynomial fits.

[David]

Thanks for your help! Sorry for the sloppy description, of course I should have written polynomial.