how can i find a fuction which define input and output of a system?

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mohammad
mohammad 2015-1-17
编辑： Image Analyst 2015-1-18
i have a system and i put some values in and get its output. for instance y=f(x) i know the values of y and x .i get y by monte carlo simaltion numerically now ,how can i find a function which is close to f ? what command can i use? i need to use the function f in another m.file

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Shoaibur Rahman
Shoaibur Rahman 2015-1-17
Use:
p = polyfit(x,y,n) % n is degree of polynomial, use a value that best fit your data
To check the fitting:
y_fit = polyval(p,x);
plot(x,y, x,y_fit)
If you are satisfied with your fitting, then your function will be:
f = p(1) + p(2)*x + p(3)*x.^2 + p(4)*x.^3 + ... + p(n+1)*x.^n
And, you can write this function in a separate m-file
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Image Analyst
Image Analyst 2015-1-17
You would never fit a 13th order polynomial. Have you ever seen what happens between and after your training points when you do that? They go haywire with enormous oscillations!
You should have some idea of the type of function you want to fit if you're looking for an analytical formula, like a polynomial or something. I have no idea what it might be because you're not sharing a plot of your data, or even the data itself so we're left to guess (or not even bother to answer which I'm sure many did).
mohammad
mohammad 2015-1-17
编辑：Image Analyst 2015-1-18
I'm really appreciated you Mr. Rahman, its result is better when I use fitting as custom equation.
But my system is a receiver including 2 parts, elementary detector and a decoder. I want to find the function f between these parts. Its curve is like image below.

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