Problem of nonlinear curve fitting

[dot27]

helo,
I am dealing with a problem of nonlinear curve fitting.
I have estimted samples of a continuous Fourier transform function, and my goal is to reach from Fourier to laplace transform using the known equality: F(S=jw)=laplace{h(t)}.
i want to represnet the laplace trnsform in the following form:
1/(as^2+bs+c), the parameters a, b, c are to be detetmined:
F(jw)*(a(jw)^2+b(jw)+c)=1,
using the eq above in all the freqenqcies F(jw) was estimated.
now i can use the method of nonlinear least squares.
how do i implement this in matlab?

Thx

 

[Valkarie]

for the help.To implement this in Matlab, you can use the lsqcurvefit() function. This function will allow you to fit a non-linear function to the data and estimate the parameters a, b, and c. You will need to define the function that you want to fit, as well as the initial values for the parameters. Then, you can call the lsqcurvefit() function, which will give you the estimated parameters. For more information on how to set up and use this function, please refer to the Matlab documentation.

 

[Mene]

for your question. Nonlinear curve fitting is a common problem in scientific research and there are various methods and tools available to address it. In your case, you are trying to determine the parameters a, b, and c in the Laplace transform equation 1/(as^2+bs+c) using samples of the Fourier transform function. This is a nonlinear curve fitting problem because the equation you are trying to fit is not a linear function of the parameters.

To implement this in MATLAB, you can use the "lsqnonlin" function which is specifically designed for nonlinear least squares problems. This function takes in the equation you want to fit, the initial values for the parameters, and the data points you have for the Fourier transform. It then uses an iterative algorithm to find the best values for the parameters that minimize the difference between the predicted values and the actual data points.

In addition to using MATLAB, there are also other software packages and programming languages that have tools for nonlinear curve fitting, such as Python's "scipy.optimize" module and R's "nls" function. It is important to carefully choose the appropriate method and tool for your specific problem and to also understand the limitations and assumptions of the chosen method. Good luck with your research!