MATLAB: Nonlinear curve fitting, how to

curve fittingMATLABmulti variablenlfitoptimization

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 ?

Best Answer

If you have the Statistics Toolbox, you should be able to do this with the nlinfit() function.

Related Solutions

MATLAB: How to find two parameters by non linear curve fitting with equation involving two variables.

Write it as a function!

function v = predicted(a,z)
% stuff
end

Then call it using the syntax explained here for either anonymmous or nested functions:

http://www.mathworks.com/help/releases/R2013b/optim/ug/passing-extra-parameters.html

MATLAB: Optimising the fit of a function with 2 variables

The function nlinfit() from the Statistics Toolbox will do this.

Here is a simple example of the use of the function:

% 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(1)
plot(x,y,'*',x,f(F_fitted,x),'g');
legend('data','nonlinear fit')

Note that I am not actually using nonlinear fitting parameters here, but I hope the idea is clear enough.

Best Answer

Related Solutions

MATLAB: How to find two parameters by non linear curve fitting with equation involving two variables.

MATLAB: Optimising the fit of a function with 2 variables

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