Nonlinear curve fitting, how to ?
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Arsalan
le 28 Juin 2014
Réponse apportée : Arsalan
le 28 Juin 2014
Hi,
I have two nonlinear functions defining the response of a system in frequency domain
H(f;Y0,Z0)= Z / ((j*2*pi*f)+(j*2*pi*f*Y0)+Z0)
H(f;Y1,Z1)= Z / ((j*2*pi*f)+(j*2*pi*f*Y1)+Z1)
to see the difference in two responses in decibles I introduce S(f) as
S(f) = 20*log(H(f;Y1,Z1)/H(f;Y0, Z0))
I also have predetermined values for S(f) obtained from experimental work where in both cases f is a known vector.
My main aim is to find values for Y1, Z1, Y0, Z0 through optimization in order to fit
S(f) = 20*log(H(f;Y1,Z1)/H(f;Y0, Z0))
to my experimental readings
How can I best achieve this ?
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the cyclist
le 28 Juin 2014
If you have the Statistics Toolbox, you should be able to do this with the nlinfit() function.
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the cyclist
le 28 Juin 2014
I expect you have a coding error. Those data look like they could be fit just fine with nlinfit, assuming you have the proper functional form defined.
Here is a very simple example of nlinfit:
rng(1)
% Here is an example of using nlinfit(). For simplicity, none of
% of the fitted parameters are actually nonlinear!
% Define the data to be fit
x=(0:1:10)'; % Explanatory variable
y = 5 + 3*x + 7*x.^2; % Response variable (if response were perfect)
y = y + 2*randn((size(x)));% Add some noise to response variable
% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x) F(1) + F(2).*x + F(3).*x.^2;
F_fitted = nlinfit(x,y,f,[1 1 1]);
% Display fitted coefficients
disp(['F = ',num2str(F_fitted)])
% Plot the data and fit
figure
plot(x,y,'*',x,f(F_fitted,x),'g');
legend('data','fit')
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