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

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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

Accepted Answer

Shoaibur Rahman
Shoaibur Rahman on 17 Jan 2015
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
mohammad on 17 Jan 2015
Edited: Image Analyst on 18 Jan 2015
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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